[Frontend] Validate post-authentication redirect targets

## Problem

Redirect query values must not permit external navigation or role-incompatible destinations.

## Relevant code

`src/pages/login.tsx, src/pages/register.tsx`

## Proposed scope

Allow only normalized same-origin application paths, preserve safe deep links, and test encoded/open-redirect payloads.

## 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/login.tsx and src/pages/register.tsx by tracing how redirect query values are read after authentication. Reproduce encoded and open-redirect payloads with focused automated tests, then verify same-origin normalized paths, safe deep links, and role-compatible destinations while running the existing related tests.

Written by the indexing model from the issue text.