Yes, it does count as relatively high magic, but the actual bonuses depend on location and time.
First of all, Forgotten Realms is what you make of it. Since you seem to be asking to determine how much magic items cost and how available they are, it is really up to you; pick according to your own campaign's needs.
If you are asking the level for the "official" Forgotten Realms, I can refer you to unofficial tweets (April 21, 2019) by Ed Greenwood, the creator (and long-time major contributor) of the setting. And the answer depends on location and time.
Q: As per 5e rules for buying an item as a downtime activity, you actually have to roll to see what items appear(better rolls, rarer items) and if a player seeks a specific one they must roll particularly high depending on rarity. There is also a bonus to represent how high/low magic the setting is, from -10 if it's super low magic to +10 if it's super high magic. What would be a reasonable bonus(if any) to add for Waterdeep in this step? ...
Ed Greenwood: Any large crossroads trading city in the Realms that attracts a lot of money will be trending towards "super high magic." As the Realms heads into the 1500s DR, I'd put Waterdeep at a +7 bonus in harsh winter height, up to +9 at end of summer when some folk want to leave and make one last "big sale" to tide them through the winter lean trading times.
The rest of the tweets are also interesting as Ed Greenwood goes on to discuss how the actual machinery runs: who are the sellers, why do they want to sell, how the auctions are run, where to find them, etc.
Yet, he finishes with a warning that is similar to what I mentioned in the beginning of this answer:
Ed Greenwood: And remember: the rules are guidelines/suggestions. When I DM, magic items are never determined by dice rolls; I place what I think best fits the campaign (often 'custom' items), and the hunt and the negotiations are roleplayed.
Other Settings
Regarding other settings, it is difficult to set a clear guidance that fits all, as fantasy, by definition, is very open to people's imagination. For example, Eberron could be considered high magic due to common-place use of magic in daily life (magic as science), yet it has been characterised as "wide magic" by its creator Keith Baker (here) and magic item availabilities are not necessarily what you would expect from a high magic setting (read here):
I don't generally see #Eberron as bleak or traditional high magic; we generally describe it as "wide magic." Effects like teleportation are rare, but lower level magic has been incorporated into everyday life.
Again set the bar according to your own gaming preferences.
