Potions of Healing are probably exempt from the magic item progression used in both the DMG and Xanathar's Guide to Everything, whether you allow them to be crafted or not.
tl;dr: Healing potions are already a special case of magic item, and the rules as written do not limit their availability. All other magic items, on the other hand, are explicitly limited. This makes controlling items-per-level/tier possible for non-healing potion items, but not for healing potions. Because the rules as written do not limit healing potion availability, healing potions counting towards a magic item limit doesn't make sense.
One of the key elements governing magic items is that, for the most part, players can't get them on their own. They expect to gain levels over time just through surviving adventuring. They expect to earn, find, or steal money, and to be able to use that money to buy things.
Magic items are explicitly different:
Unless you decide your campaign works otherwise, most magic items are so rare that they aren’t available for purchase. (DMG, chapter 7, Magic Items, Buying and Selling)
And immediately following that line, an exception is made for common items, specifically using healing potions as an example:
Common items, such as a potion of healing, can be procured from an alchemist, herbalist, or spellcaster. (DMG, chapter 7, Magic Items, Buying and Selling)
This special category is also found in XGtE, and the special treatment of potions of healing is extended even further. Nearly everything about potions of healing is marked out as an exception to the rules given in XGtE. These exceptions have a mechanical impact of making the potions more available to players than other magic items.
Notably, the rules as written in XGtE include explicit suggestions to limit players' ability to craft magic items and these suggested limitations are explicitly waived for potions of healing. Other magic items require formulae (a pure plot element-- the DM includes them in the game, or not), exotic components ("invariably" required, and getting them is suggested to be part of adventuring, which requires the DM to plan and run that portion of the adventure), and a nontrivial amount of downtime (variably available, and down to DM choices regarding in-game scheduling).
So crafting most magic items, with rules as written, requires explicit DM approval and action to make possible, and this requirement is what makes the limitation of magic item quantity and rarity possible. Further, the crafting cannot fail-- if PCs get the components and the time, the item will come to them.
All of this leads me to:
Conclusion 1: Potions of healing are categorically different from mother magic items, whether we're considering crafting or not.
The most reasonable view of a table like the Magic Items Awarded by Tier in XGtE seems to me to be about what players have, not what the DM bestows. Consider a case in which players complete an adventure and find a treasure hoard worth 25,000 gp, in accordance with the DMG or XGtE guidelines for rewards, but they arbitrarily decline to take any of it. Hard to imagine, I know!
The DM has fulfilled their duty and provided an appropriate reward, but game mechanics which depend on wealth per level assume that PCs actually have that wealth, not just that the DM made it available at some point.
If a player already has 10 major magic items at level 4 via crafting, I suggest that it is not more appropriate to award an additional two major magic items rather than zero, simply because that's what the table says the DM should award-- the 11th and 12th magic items are far more marginal than the first two at that level of abstraction. The act of the DM granting magic items seems far less important to the game than the PCs having them, however obtained.
Conclusion 2: The assumption of adventuring rewards is that PCs have them, not that they were offered.
Opportunity costs are uneven. Downtime is not uniformly available or useful. Individual games vary, of course, but in most that I've seen or heard about downtime is either not used to any purpose (it's fast-forwarded), not discussed at all, or is included only when a player has something they'd specifically like to do with it. In such a game, the downtime investment is negligible: if you aren't going to use it to craft a magic item, what else would you use it to do, if anything?
Resources like money, as above, are expended for adventuring (among other purposes). It's not clear that the cost of Adventure A, which features magic item Z as a reward, is more profitable than Adventure B, which features the ingredients required to make magic item Z among its rewards, when downtime is cheap and crafting is riskless (in terms of outcome).
Unless the adventures are designed in a particularly lopsided way, there is no inherent reason that getting a magic item through one method is strictly better or worse than the other. It seems to me to be largely a question of narrative and flavor.
Conclusion 3: The investment of resources in finding a magic item as treasure while adventuring versus risklessly crafting it using the rewards of adventuring seems similar either way.
Most in-game rewards are expected to do things, not simply exist. There are obvious exceptions, like the Cloak of Billowing, but many magic items are legitimately useful in game-mechanical terms, like a +1 longsword.
If we're already using the XGtE rules for magic item progression, then we're in the realm of the DM picking specific magic items to give to the PCs. That means that it's on the DM to make those rewards useful or valuable. Giving a character that can already cast Disguise Self a Hat of Disguise is a bit redundant. Not useless, but less of a reward than might have been expected.
So a reasonable presumption is that the DM will choose meaningful magic item rewards valuable to the party and/or individual PCs. It is reasonable to think that players wanting to craft magic items will be similarly motivated-- they want to get something useful at the end.
Either process is unlikely to generate a whole lot of "useless" magic item rewards, absent a serious miscalculation, and that becomes more true as PCs get rarer magic items.
For such items there is an obvious mechanical reason to limit access. For the same reason level 2 PCs shouldn't expect to stumble across 1,000,000 gp, they shouldn't expect to have dozens of mechanically useful magic items. There is definitely wiggle room, and I wouldn't expect a couple of items to tip the scales too much. But I'm not sure I agree that the intent of the crafting rules is to allow players to get some arbitrary number of "bonus" magic items at their discretion, any more than any other rule allows them to declare that they've gained a class level or feat.
Conclusion 4: Suggested item rewards by level/tier seem meant to allow for interesting rewards while also limiting PC resources and power to lie within restricted ranges. If that's true, then allowing PCs to have extra magic items (by any means) makes them "too powerful" for the intended rules. If it's not true, then I don't see what those tables are for at all.
Finally, and this is an easy one, there is no way to obtain a magic item with the DM explicitly allowing it. If a player says "I would like to craft magic item X", and the DM says "no", then the PC won't get that item from crafting. If a player says "I would like to find magic item X while adventuring" and the DM says "no", then the PC won't get that item from adventuring. It is also true, in an ancillary capacity, that PCs cannot accumulate resources of any sort without the DM's explicit approval and inclusion of those resources.
Because DMs must explicitly approve a magic item's presence (via crafting or loot), must provide the scenario to find the item or its ingredients, and crafting is a riskless process, allowing a player to craft the item is tantamount to simply placing it as treasure. The DM makes the item available, one way or the other, and then the PC gets that item.
Conclusion 5: There is no real difference in how a magic item makes it into the game: the DM allows it, and makes it available to the relevant player.
So, looking at each of the above conclusions in turn,
- The tables in XGtE assume that PCs actually have what was given to them by
- PCs need to invest resources in obtaining magic items, whether found
as loot or crafted
- Magic items that don't affect game mechanics aren't unbalancing, but
magic items that do affect game mechanics can be
- Magic items, particularly rarer ones, are intended to be valuable and
useful to characters
- Having more magic items that affect game mechanics results in a
"stronger" character than one that has fewer
- PCs cannot obtain magic items of any sort by any means without the DM
explicitly allowing each one
hopefully my overall arguments become clearer:
Nearly all magic items are intended to give some benefit to PCs, with more items generally meaning more benefits. A PC can only realize those benefits by having and using the magic items. Magic items, as loot rewards or crafting outcomes, require resource investment from PCs either way, and neither is clearly a "better deal", in terms of resource investment, than the other. All magic items that are in a given game come from explicit, case-by-case DM approval-- there is no other way to get one, and the DM has the same decisions to make whether it's crafted or found.
Therefore, the XGtE magic item guidelines are more sensibly interpreted as the quantity of magic items a PC has, rather than just the number that the DM has included as arbitrary rewards available to that PC. Given that adventuring is required either way, and crafting cannot fail, either case can be viewed as the DM granting an item to a PC.
So my conclusion is that crafted magic items in general should be counted against the suggested number of such items per level in the XGtE chart. They work the same way, and have similar impacts on a game, no matter how a PC comes to own one.
However, because healing potions are explicitly separated from the factors which limit production of other magic items, there is little to no RAW way for a DM using the XGtE magic item crafting rules to limit how many of them players want to make.
If they have the money (which they likely will, at 25g/basic potion, or level-appropriate wealth for rarer potions), herbalism kit (and proficiency with it), and some downtime (which does not need to be in unbroken, 8 hour periods per day), there are few levers left for the DM to control to limit production in the ordinary course of play for many campaign types. This is very similar to the information in the DMG, which suggests that if a PC can find an apothecary or herbalist shop, and have the money, they can buy healing potions.
Because campaigns, generically, do not include guidelines for how long they should take (in-game time) or at what pace they should proceed, the rules for healing potion brewing suggest that players are limited by those factors only. And even while brewing healing potions becomes less convenient for rarer potions, they are still far easier to produce than non-healing potion items of equivalent rarity.
So crafted healing potions should not count against suggested magic item limits, not because they were crafted by PCs, but because they are healing potions.