[Frontend] Fix exhaustive-deps violations in surgery and email verification flows

## Problem

Effects omit referenced callbacks, allowing stale closures and unpredictable reruns.

## Relevant code

`src/pages/surgeries.tsx, src/pages/verify-email.tsx`

## Proposed scope

Stabilize callbacks or redesign effects, then test route changes, retries, and unmount behavior.

## Acceptance criteria

- [ ] The reported behavior is reproduced or characterized with a focused automated test before the fix.
- [ ] The implementation satisfies the proposed scope without weakening TypeScript, lint, authorization, privacy, or error handling.
- [ ] Success, empty/loading where applicable, failure, and boundary cases are covered.
- [ ] Existing related tests pass and new regression coverage is included.
- [ ] User-facing behavior remains accessible by keyboard and at mobile viewport sizes where UI is affected.
- [ ] Documentation is updated when the change alters configuration, contracts, security assumptions, or contributor workflow.

## Contributor notes

Base the work on the latest `main` branch. Keep unrelated refactors out of the pull request and include screenshots or recordings for visible changes. Never use real pet, medical, contact, wallet, or credential data in fixtures.

Start in src/pages/surgeries.tsx and src/pages/verify-email.tsx by locating the effects with exhaustive-deps violations and characterizing the reported behavior with focused automated tests. Check route changes, retries, unmount behavior, and relevant success, empty/loading, failure, and boundary cases. Done means the effects no longer permit stale closures or unpredictable reruns, regression coverage is included, and related tests pass.

Written by the indexing model from the issue text.