Code Review Bench PR #26694 - refactor: Remove trpc/react dependency from @calcom/atoms

[tomerqodo]

Code Review Bench PR calcom#26694

Original PR Title: refactor: Remove trpc/react dependency from @calcom/atoms
Original PR Description: ## What does this PR do?

Decouples trpc from platform atoms by moving the useTeamMembersWithSegment hook into the web app and removing trpc references in atoms. This reduces cross-package coupling with no behavior changes.

• Refactors
  • Moved useTeamMembersWithSegment to apps/web/modules/event-types/hooks.
  • Exported UseTeamMembersWithSegmentProps and useProcessTeamMembersData from atoms.
  • Removed trpc usage from atoms; platform hook stays as useTeamMembersWithSegmentPlatform.
  • Updated EditWeightsForAllTeamMembers to use the new web hook and corrected platform import path.
  • Replaced TRPC types in AvailabilitySettings with repository types and removed trpc/react from atoms tsconfig.

Impact

Mandatory Tasks (DO NOT REMOVE)

• I have self-reviewed the code (A decent size PR without self-review might be rejected).
• N/A - I have updated the developer docs in /docs if this PR makes changes that would require a documentation change. If N/A, write N/A here and check the checkbox.
• I confirm automated tests are in place that prove my fix is effective or that my feature works.

How should this be tested?

• Please use the latest Vercel preview and test please 🙏.

Original PR URL: calcom#26694