[Frontend] Centralize authenticated fetch and token refresh behavior

## Problem

API modules implement authentication and errors inconsistently, inviting missed headers and refresh races.

## Relevant code

`src/contexts/AuthContext.tsx, src/lib/api`

## Proposed scope

Provide one typed request client with single-flight refresh, abort support, normalized errors, and tests for concurrent 401 responses.

## 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 by reading src/contexts/AuthContext.tsx and the modules under src/lib/api to map the existing authentication and error behavior. Add a focused automated test that characterizes concurrent 401 responses, then verify the typed client covers refresh, abort, normalized errors, and the listed success, loading, failure, and boundary cases without breaking related tests.

Written by the indexing model from the issue text.