Refactor batched serial pbtrs implementation details and tests

[yasahi-hpc]

This PR aims at improving the implementation and testing of serial pbtrs.

• Implementation details are inside Impl namespace.
• Remove using namespace KokkosBatched from the test code
• Rename variables starting from underscores in the test code
• Remove the dependency to pbtrf from the pbtrs analytical tests (see the discussions in fix: getrs serial internal implementations #2488)
• Move test specializations from Test_Batched_SerialPbtrs_Real.hpp and Test_Batched_SerialPbtrs_Complex.hpp into Test_Batched_SerialPbtrs.hpp.
• Add docstring and assertion for Arg template parameters