[Epic 953][Stage III][cloud-api] Remove stateful APIs

Parent epic: nearai/cloud-api#953
Stage: Stage III (Nov 1st) - remove stateful APIs and shut down Private Chat
Component: cloud-api

Scope

Remove the cloud-api stateful API surfaces only after the Stage I migration/export window is closed, Stage II database work is complete, and the Chat account-deletion worker no longer depends on Cloud Conversation/File DELETE routes. If that worker is replaced, the replacement or final-cleanup path must be verified before the retained DELETE routes are removed.

Action items

• Remove Conversation APIs.
• Remove Files APIs.
• Remove other conversation-related APIs such as copy, pin, archive, and related stateful operations.
• Retire the Stage I resource DELETE exceptions only after the account-deletion lifecycle condition above is satisfied.

Acceptance criteria

• No write or read API remains for retired stateful conversation/file surfaces in cloud-api after the export window and account-deletion lifecycle are complete.
• DELETE /v1/conversations/{conversation_id} and DELETE /v1/files/{file_id} are not removed until the Chat worker is retired or replaced and the final account-deletion or cleanup path has passed end-to-end verification.
• OpenAPI/docs/tests no longer advertise or rely on removed stateful APIs.
• Any retained Responses API path is stateless and does not persist Conversation data.