[Frontend] Repair the root type-check command and enforce it in CI

## Problem

The documented npm run type-check currently fails, so regressions can merge unnoticed.

## Relevant code

`package.json, tsconfig.json, .github/workflows`

## Proposed scope

Resolve current errors, ensure the command targets intended frontend files, and add a required CI job with actionable output.

## 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 running the documented npm run type-check command and inspect package.json and tsconfig.json to characterize the current errors and intended frontend scope. Then review .github/workflows for the appropriate CI entry point. Done means the command succeeds against the intended files, its regression coverage is included, and a required CI job reports actionable failures.

Written by the indexing model from the issue text.