Yes it does, at the top of every chat there is a drop-down to select the model, which displays the current model. It's been a constant part of the UI since forever.
Logged in, non paid account, on a desktop, for me, it's exactly as the person you're replying to has stated.
If I log out, it shows 4o mini, and when I try to change it, it asks me to login or sign in rather than giving me any options.
When I use enough chatgpt when logged in it gives me some nebulous "you've used all your xyz tokens for the day". But other than that there is no real signal to me that I'm getting a degraded experience.
> With a free account the model it claims to be using is "4o auto", which is not a model but apparently an attempt to automatically decide models for you to be more cost effective.