refactor: add AIContextManager to Duo Chat Controller

Description

This begins implementation of &14735.

Since Duo Chat must now interact with the language server, we must add the client to the chat controller class.

closes gitlab#480792 (closed)

note: I did not add it to the DependencyContainer since the dependency container is a dependency of the language server itself. I think it's best to wait until @viktomas 's DI framework is introduced to this codebase.

note: only targeting desktop at this time

Testing

NA. There is no functionality change.

Screenshots (if appropriate)

What CHANGELOG entry will this MR create?

• fix: Bug fix fixes - a user-facing issue in production - included in changelog
• feature: New feature - a user-facing change which adds functionality - included in changelog
• BREAKING CHANGE: (fix or feature that would cause existing functionality to change) - should bump major version, mentioned in the changelog
• None - other non-user-facing changes