fix(formulas): replace hardcoded ~/gt/ paths with $GT_ROOT (#758)

* fix(formulas): replace hardcoded ~/gt/ paths with $GT_ROOT

Formula files contained hardcoded ~/gt/ paths that break when running
Gas Town from a non-default location (e.g., ~/gt-private/). This causes:

- Dogs stuck in working state (can't write to wrong path)
- Cross-town contamination when ~/gt/ exists as separate town
- Boot triage, deacon patrol, and log archival failures

Replaces all ~/gt/ and $HOME/gt/ references with $GT_ROOT which is
set at runtime to the actual town root directory.

Fixes #757

* chore: regenerate embedded formulas

Run go generate to sync embedded formulas with .beads/formulas/ source.

internal/formula/formulas/mol-shutdown-dance.formula.toml

@@ -8,7 +8,7 @@ goroutine (NOT a Claude session) that runs the interrogation state machine.
 
 Dogs are lightweight workers in Boot's pool (see dog-pool-architecture.md):
 - Fixed pool of 5 goroutines (configurable via GT_DOG_POOL_SIZE)
-- State persisted to ~/gt/deacon/dogs/active/<id>.json
+- State persisted to $GT_ROOT/deacon/dogs/active/<id>.json
 - Recovery on Boot restart via orphan state files
 
 ## State Machine
@@ -151,7 +151,7 @@ If target doesn't exist:
 - Skip to EPITAPH with outcome=already_dead
 
 **3. Initialize state file:**
-Write initial state to ~/gt/deacon/dogs/active/{dog-id}.json
+Write initial state to $GT_ROOT/deacon/dogs/active/{dog-id}.json
 
 **4. Set initial attempt counter:**
 attempt = 1
@@ -477,11 +477,11 @@ bd close {warrant_id} --reason "{epitaph_summary}"
 
 **3. Move state file to completed:**
 ```bash
-mv ~/gt/deacon/dogs/active/{dog-id}.json ~/gt/deacon/dogs/completed/
+mv $GT_ROOT/deacon/dogs/active/{dog-id}.json $GT_ROOT/deacon/dogs/completed/
 ```
 
 **4. Report to Boot:**
-Write completion file: ~/gt/deacon/dogs/active/{dog-id}.done
+Write completion file: $GT_ROOT/deacon/dogs/active/{dog-id}.done
 ```json
 {
   "dog_id": "{dog-id}",