chore: remove example/ai-agent-app and root taskiq_poc.py

[tmgbedu]

What

Deletes two unused paths cleanly:

1. example/ai-agent-app/ — the entire example directory (27 files)
2. taskiq_poc.py — the repo-root proof-of-concept script

References removed

None needed beyond the files themselves. Confirmed no external references exist:

• Workspace — fastapi_startkit/pyproject.toml uses a glob (members = ["application", "example/*"]), no explicit ai-agent-app entry. ai-agent-app was a standalone project (own uv.lock) and never appeared in fastapi_startkit/uv.lock.
• CI — .github/workflows/test.yml builds config-app, database-app, and agents; it never referenced ai-agent-app.
• Docs — no references to either path.
• taskiq_poc.py had no importers anywhere.

Verification

• grep -rn ai-agent-app . (excluding .git and .claude/worktrees) → 0 matches
• grep -rn taskiq_poc . (same exclusions) → 0 matches
• uv sync --group dev in fastapi_startkit/ → exit 0, resolves cleanly

[tmgbedu]

✅ Code review verdict: APPROVE (posting as comment — GitHub blocks self-approval on own PR).

Pure-deletion PR (0 additions / 4775 deletions across 27 files). Verified independently:

• grep -rn ai-agent-app and grep -rn taskiq_poc (excluding .git/.claude) → only matches are inside the deleted files themselves; no external references remain.
• No taskiq dependency declared in any pyproject.toml — POC was standalone, removal is clean.
• CI (.github/workflows/test.yml) builds example/config-app, example/database-app, and example/agents — never ai-agent-app. example/agents is a separate, still-existing directory and is unaffected.
• Workspace glob members = ["application", "example/*"] needs no edit; the deleted dir simply stops matching.
• No framework/core code touched — no correctness, SQL/ORM, NULL-handling, or test surface impacted.

Clean removal. LGTM.