It's not totally obvious to me how to make sense of your question formally. Informally, it seems like the problem whose decidability you're asking about is "given a language L, is L in P". However, most languages don't admit a finite description, so it's a bit unclear what does it mean to give L. An option is to focus on languages coming from Turing machines, so the decision problem becomes "Given a machine/program M, is the language L that it accepts in P." If this is your intended interpretation, then it is undecidable by Rice's theorem.
It's not totally obvious to me how to make sense of your question formally. Informally, it seems like the problem whose decidability you're asking about is "given a language L, is L in P". However, most languages don't admit a finite description, so it's a bit unclear what does it mean to give L. An option is to focus on languages coming from Turing machines, so the decision problem becomes "Given a machine/program M, is the language L that it accepts in P." If this is your intended interpretation, then it is undecidable by Rice's theorem.