[Feature]: Add session persistence for unimplemented LLM providers

#443 added session persistence for Gemini, but other providers were left unimplemented.

We should add similar implementation for other providers, where Initialize() will convert api messages to provider-specific messages and add them to the chat history. We should add this for all the providers that don't have them, and keep it in mind for any future providers added.

Adding tests is also very welcomed. Basic flows like saving and loading sessions, creating a new session, deleting a session, and listing sessions should be covered. Edge cases like invalid session ID and corrupted save file should also be covered.