Complete three-tier config migration (gt-k1lr)

- Add doctor checks for new config architecture:
  - SettingsCheck: Verify rigs have settings/ directory
  - RuntimeGitignoreCheck: Verify .runtime/ is gitignored
  - LegacyGastownCheck: Detect/remove old .gastown/ dirs
- Update .gitignore to include .runtime/
- Update architecture.md with new directory structure
- Update hq.md to clarify PGT vs GGT config locations

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

docs/hq.md

@@ -131,12 +131,16 @@ Sometimes you need to run multiple Gas Town systems from the same parent directo
 If Python Gas Town (PGT) and Go Gas Town (GGT) both use `~/ai/`:
 ```
 ~/ai/
-├── .gastown/           # PGT config
+├── .gastown/           # PGT runtime config (hidden)
+├── .runtime/           # GGT runtime state (gitignored)
 ├── .beads/             # Which system owns this?
 ├── mayor/              # PGT mayor? GGT mayor?
 └── gastown/            # PGT rig? GGT rig?
 ```
 
+Note: GGT uses `.runtime/` for runtime state and `settings/` for behavioral config.
+PGT uses `.gastown/` for both.
+
 ### Solutions
 
 **Option 1: Separate HQs (recommended)**