socket_processor: Enforce inline rules

This change moves the global `processor` pointer into the
`SocketProcessor` class as a private static inline member.

This refactoring improves code quality by:
- Eliminating a global variable, which reduces namespace pollution.
- Enhancing encapsulation by managing the singleton instance within
  its own class.
- Making the code cleaner and more maintainable.

Bug: 438841609
Test: atest bluetooth_hal_socket_processor_test
Flag: EXEMPT, refactor.
Change-Id: Iee23e20ad6fc208cdebefc3f678795a6731731cf
2 files changed