Reorganize integration tests by feature and contract

> [!IMPORTANT]
> Reserved for @cv. Do not self-assign this issue. Do not open an implementation PR unless @cv requests help.

Parent: #7691

## Problem

The root `test/` directory contains more than 600 files. Feature tests, package contracts, documentation checks, security tests, and workflow tests live together.

## Scope

- Group integration tests by feature.
- Group cross-cutting tests by contract.
- Preserve co-located unit tests.
- Keep Vitest projects disjoint and exhaustive.

## Acceptance criteria

- Integration and contract ownership is visible from each path.
- Vitest project membership remains disjoint.
- Watch triggers map opaque inputs to the new paths.
- Test titles and imports remain behavior-oriented.
- The root test-file budget decreases.