I'm looking for an app that after I play a game of chess (or 3) will tell me if I'm a beginner or intermediate. Not looking for an app to teach me or to assess the game move by move. Does anyone know the best chess app (for Android) for this?
There is no "best app". However the chess.com app should give you a reasonable guesstimate after 5 games. After 24 your rating will be more refined. 3 chess games is generally not enough to (accurately) determine your skill. If you don't like chess.com there are plently of others, such as lichess and chess clock.
No app will give you a better assessment than what you'd get from asking a random human chess player. There are just too many unknowns:
First, there's no objective definition of a barrier between beginner and intermediate. If an app like the one you ask for existed, it'd just be taking the developer's personal opinion as fact and giving you an answer from there.
There's also the problem that chess engines don't really have a concept of difficulty. It's possible to take a game and calculate by how much it deviates from the perfect-ish play of a computer, but it won't know how likely other humans are to make similar mistakes.
Finally, chess engines are designed to assess individual positions. Any criteria you use to aggregate over an entire game will be arbitrary.
In short, since the answer to your question will always be subjective, you may just as well answer a bunch of us directly for our opinions rather than using a piece of software as an intermediary. Would you mind showing some of your games?