As I mention in my other answer, while there is a way to calculate a given character's CR as if they were an NPC using the guidelines on DMG p.274, there's no particular table for determining what a 'medium' difficulty encounter is for a creature of a particular CR. As such, finding out your effective CR isn't particularly useful for encounter building.
I've spent some time running through the encounter building & CR calculation math to see if it's actually reasonable to create such a table, and have come up with something that may be useful as a very rough guideline if you're at the point where you're calculating your party members' CR because they're performing so differently from expectations at their level.
Building the Table
In order to try and map CRs to difficulty, I had to find a way to combine the method of calculating CR and the encounter building math. In order to do so, I had to estimate the CR of a 'default' character of a given level.
To build these estimates, I used the CR calculation guidelines from DMG p.274 on a Variant Human Fighter (Champion), with starting (relevant) stats of 16 Str & 14 Con, and the Tough feat. I chose these options so that as many features of the character as possible factor flatly into the CR calculating math, as Champions are one of the most consistent/least resource based subclasses and trying to account for a full set of limited/resource based character features in a CR calculation introduces more variables.
The fighter is equipped with a morningstar, shield, and chainmail. For character progression, he gains +2 Str at 4 and 6, then +2 Con at 8, 12, and 14. I ignore the remaining two ASIs as other stats don't affect these calculations, and there are few feats remaining that would affect CR calculations. He gains splint armor at 5 and plate at 11. He begins with the Defense fighting style, then takes Dueling as his additional one at level 10.
When calculating this character's effective CR, I mostly do not take any limited-use features into account for CR calculation purposes (these being Second Wind, Action Surge, Indomitable, & Survivor).
The exception to this is that for levels 17+, I assume the first round of each combat uses Action Surge to Attack which increases expected damage by 1/3 (Overall Damage Output, DMG p.287) and increases the calculated CR of levels 17-20 by 1 (and +10% for expanded critical would actually bump level 20 up by an additional 1, if you wish to account for that). The reason for this is because 17+ is when you can use it twice per rest. Since the 'minimum' guideline for encounters per adventuring day is 6 and the expected number of short rests is ~2, this is when you can roughly assume one use per combat.
The expanded critical strike range I don't take into account because even adding +10% to expected damage to account for it doesn't seem to push any calculated CRs up to the next tier (level 20 aside, as mentioned above).
To calculate the value for ~'Medium' difficulty CR, I simply use the encounter building guidelines as if a solo character of that character level was fighting a solo creature (using the 1.5x multiplier, as per the guidelines on DMG p.82-83.).
I pick the highest value CR # that isn't 'hard' (usually this is 'medium', but in the case of levels 3 and 9 I believe there is no CR that is 'medium' for them as a solo monster, only 'easy' and 'hard').
If you wish to use this for purposes other than solo PC vs. solo monster, you may wish to use the XP Thresholds By Character Level table on DMG p.82 and map that to the effective character CRs for that character level. (I didn't wish to reproduce that here as it seems to specifically be a table that WOTC has been avoiding making freely available in their free PDFs, and also it's an even larger table to copy down)
\$\begin{array}{r||c|c|}
&\text{Effective Character CR}&\text{~'Medium' difficulty CR}\\\hline\hline
1&1&1/4\\\hline
2&1&1/2\\\hline
3&1&1/2\\\hline
4&2&1\\\hline
5&3&2\\\hline
6&4&2\\\hline
7&4&3\\\hline
8&5&3\\\hline
9&5&3\\\hline
10&6&4\\\hline
11&7&4\\\hline
12&8&5\\\hline
13&8&5\\\hline
14&9&6\\\hline
15&9&6\\\hline
16&9&7\\\hline
17&11&8\\\hline
18&11&8\\\hline
19&12&8\\\hline
20&13&9\\\hline
\end{array}\$
(As a quick, rough sanity check, we can do the math and see that a level 20 character fighting a solo CR 13 is considered a 'deadly' encounter, which would likely be the appropriate descriptor for a fight where a character fights itself given that we've calculated a level 20 as being CR 13.)
Conclusion, Summary, & Precautions
As a rough guideline, it seems accurate to say if you calculate a character as being CR 5-9, a good medium matchup against them (solo) is 2-3 CR below them. At CR10+, that seems to grow to 3-4. Below CR 5, it's a bit murkier, but 2 CR steps below them still seems safe, if not easy. Unfortunately, we can't really extrapolate past level 20, so if a party member is performing well and above CR13 there's not much we can do to map them to a 'medium' encounter in this fashion.
A big problem here is that CR is a relatively 'low-resolution' measurement, even compared to character level. We can see this with how effective character CR 9 maps to ~'Medium' CR 6 & 7, and this character is CR 9 at character levels 14, 15, & 16. As a result, it could be hard to tell if the party is at the 'high end' of CR 9 or the 'low end'.
I believe this issue is also compounded when converting through the two tables- both are meant as guidelines and good estimates, but the 'estimate' part gets even blurrier when you're trying to convert through two previously-unrelated tables like this. This is especially true when using only a single character like this as the anchoring point between the two tables- fighters might fall very high or low in their character level -> CR conversion ratio compared to other classes.
I may also just be outright making a mistake in the calculations if the class features I've ignored have a bigger impact than I expect on CR, though I imagine it'd be +1 CR at most at higher levels if so. If I had the time, I'd do this for each character class to get a better overall estimate of character level ~-> CR, but this took quite a bit as-is.
I believe there's also just some inherent risk in using the CR calculation guidelines on PCs; it becomes very clear that PCs have significantly different ratios of offense and defense compared to a typical monster, to the point where the difference between the sample character's calculated offensive & defensive CR was as large as 4 at points, and that may be larger than the expected/tolerated difference between offense & defense for sane CR calculations.
Ultimately, those calculations are meant for use on NPCs- they don't take into account such things as having to go through multiple fights, having hit dice for resting between them, and potentially having no resources when starting a fight; They're meant for monsters that are there for a single encounter.
That all said, the rough guideline should serve as a decent starting point and still leave you with breathing room to adjust for encounters past the first one, so long as you take stock of how the party performed.