sessions: centralize context key definitions into common/contextkeys.ts (#306439)

Move RawContextKey definitions for active session state (provider ID, type,
background provider, git repository, chat session provider ID) from
sessionsManagementService.ts and copilotChatSessionsActions.ts into the
shared sessions/common/contextkeys.ts module. Replace hardcoded context
key strings with .key property access in all consumers.

Co-authored-by: Copilot <[email protected]>