How to prove computational completeness of a variant of P system
When you have studied a lot of papers, as you say, then you must have seen how it works. You prove a system to be computationally complete by showing how your new system is able to simulate a Turing machine. Instead of a Turing machine you can use any computational model that in itself is computationally complete, like counter automata (register machines) for example.

In P system theory there are many variants, some work on strings, other on numbers. The model you choose to simulate ideally must match that domain.

So, you do not use "formal language" as such, but only the models studied by formal language theory.