You shouldn’t switch from search to P-Max, you should complement search with P-Max. P-Max for lead-gen is designed to utilize data from your existing search campaigns. If you stop running search completely P-Max probably won’t run very efficiently.
I would also recommend against letting P-Max run your branded search ads. This should always be run in a separate search campaign so you can have a much better idea of what your CPAs are for branded vs. topical search, plus you can have better control over your branded spend.