Hi Alex,
No problem about the delay, but I appreciate your consideration.
If you think that the first proposal could complicate things then it is better the second approach.
I checked on the link you provided and it looks good. Just maybe adding a line on top of the suggestions with a different color telling the user for example “Recently used” or similar, in order to not confuse him about thinking that it is a search among all existing users in the site.
Regarding this method, do you think it could interfere with some other existing function used in wp or some popular plugins?
This can be a good add, if possible.
Thanks Alex as usual
Best regards