Setup GitHub action that verifies new e2e tests are written with every new feature

### What is this about?

We want to have an automated check in place to prevent engineers from merging new features without adding new tests (unit, e2e, api, etc.). This check would encourage engineers to include new tests alongside new features proactively.

### Scenario

_No response_

### Design

_No response_

### Technical Details

_No response_

### Threat Modeling Framework

_No response_

### Acceptance Criteria

_No response_

### Stakeholder review needed before the work gets merged

- [ ] Engineering (needed in most cases)
- [ ] Design
- [ ] Product
- [ ] QA (automation tests are required to pass before merging PRs but not all changes are covered by automation tests - please review if QA is needed beyond automation tests)
- [ ] Security
- [ ] Legal
- [ ] Marketing
- [ ] Management (please specify)
- [ ] Other (please specify)

### References

_No response_

No files, tests, or entry points are named in the issue, and its acceptance criteria are empty. First map the repository's existing GitHub Actions and test suites, then define how a feature change is identified and which test coverage is required. Done means the automated check reliably blocks or flags qualifying changes without tests.

Written by the indexing model from the issue text.