[Cases] Refactor case client

[jonathan-buttner]

The cases plugin needs to support a contract between plugins in addition to a REST API to interface with the UI. To avoid duplicating the functionality in both the REST APIs and the contract, we'll want to move the functionality to a common place. This common place is the client.

Refactor the case client to have all the HTTP routes implementation. This removes duplication of the functionality and allows a single place to implement the permissions check for each route.

Also, all unit tests should be converted to integration tests as part of the refactoring.

Routes to migrate:

• (Case connector feature) Sub cases (PR: [Cases] Migrate sub cases routes to a client #96461)
• Comments (PR: [Cases] Move remaining HTTP functionality to client #96507)
• Configurations (PR: [Cases] Move remaining HTTP functionality to client #96507)
• Cases (PR: [Cases] Move remaining HTTP functionality to client #96507)
• Tags (PR: [Cases] Move remaining HTTP functionality to client #96507)
• Status stats (PR: [Cases] Move remaining HTTP functionality to client #96507)
• Reports (PR: [Cases] Move remaining HTTP functionality to client #96507)

[elasticmachine]

Pinging @elastic/security-threat-hunting (Team:Threat Hunting)

[elasticmachine]

Pinging @elastic/security-solution (Team: SecuritySolution)

[cnasikas]

Implemented in #95058