There are framework proficiency levels across different organisations. I always find the CEFR markers as fairly decent.
In my opinion I would class B2 as being fluent enough to claim that you can speak a language "fluently". That is an accurate claim. C2 is essentially language mastery, native speaker level but perhaps with a discernible accent. The only language I definitely speak at that level is my native English.
I think the accent isn't that relevant to determine categories, unless it prevents whoever you are talking with from understanding you.
For example I'd say my Italian is probably between B2 and C1. I'd say my English on the other hand is likely at C2. But my Italian accent is far better than my English / American accent. I've had Italians try and guess where in Italy I was from. They hear a slight accent, but they don't necessarily categorise it as foreign.
I don't know why by the way, the accent just comes more naturally to me.
At the same time I am completely unable to pronounce a French R correctly. Doesn't matter what I say in French, as soon as there's an R in it, I sound like an idiot.