[rd-code-23]

Summary

• allow users to rename custom exercises from the Configure Exercise page
• keep the user on Configure Exercise after saving the new name
• add an authenticated, ownership-protected PATCH endpoint
• update the TanStack Query cache after a successful rename
• remove duplicated exercise names from the RHF routine draft
• derive names reactively from the existing exercise cache without fetching from the routine editor

State ownership

TanStack Query owns server-derived exercise names. React Hook Form stores only the exercise reference and routine-specific configuration. The routine editor observes existing cached exercise data with an explicitly disabled query, so cache updates remain reactive without initiating exercise API requests.

Security

The update operation matches both the exercise ID and authenticated owner ID. Built-in exercises and exercises owned by another user cannot be renamed.

Verification

• contract tests pass
• API tests pass
• web tests pass
• API and web typechecks pass
• API and web lint pass