[Python] Make FlightError a non-cdef class

[mroeschke]

Describe the enhancement requested

Part of #50398, FlightError in python/pyarrow/_flight.pyx is a cdef class that inherits from Exception. Cython currently doesn't support building with the Limited API for these types. It appears possible to maintain the same inheritance as a plan Python subclass and pull out the extension code into it's own cdef function.

Component(s)

Python