[Frontend] Align Next.js and eslint-config-next major versions

## Problem

The app uses Next 16 while eslint-config-next remains on 15.2.0, risking incompatible rules and parser behavior.

## Relevant code

`package.json`

## Proposed scope

Upgrade to compatible versions, document the supported matrix, and verify lint, type-check, test, and production build.

## 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 with package.json on the latest main branch and inspect the Next.js and eslint-config-next versions and available scripts. Align the major versions, document the supported version matrix, and verify lint, type-check, test, and production-build commands. Done means the compatibility issue is addressed and the required checks pass without unrelated changes.

Written by the indexing model from the issue text.