fix: prevent inherited BEADS_DIR from causing prefix mismatch (#321)

- Fix beads.run() to always explicitly set BEADS_DIR based on the working
  directory or explicit override
- This prevents inherited environment variables (e.g., from mayor session
  with BEADS_DIR=/home/erik/gt/.beads) from causing prefix mismatch errors
  when creating agent beads for rigs
- Update polecat manager to use NewWithBeadsDir for explicitness
- Add comprehensive test coverage for BEADS_DIR routing and validation
- Add SessionLister interface for deterministic orphan session testing

Root cause: When BEADS_DIR was set in the parent environment, all bd
commands used the town database (hq- prefix) instead of the rig database
(gt- prefix), causing "prefix mismatch: database uses 'hq' but you
specified 'gt'" errors during polecat spawn.

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

internal/doctor/orphan_check.go

@@ -17,9 +17,23 @@ import (
 // the expected Gas Town session naming patterns.
 type OrphanSessionCheck struct {
 	FixableCheck
+	sessionLister  SessionLister
 	orphanSessions []string // Cached during Run for use in Fix
 }
 
+// SessionLister abstracts tmux session listing for testing.
+type SessionLister interface {
+	ListSessions() ([]string, error)
+}
+
+type realSessionLister struct {
+	t *tmux.Tmux
+}
+
+func (r *realSessionLister) ListSessions() ([]string, error) {
+	return r.t.ListSessions()
+}
+
 // NewOrphanSessionCheck creates a new orphan session check.
 func NewOrphanSessionCheck() *OrphanSessionCheck {
 	return &OrphanSessionCheck{
@@ -33,11 +47,21 @@ func NewOrphanSessionCheck() *OrphanSessionCheck {
 	}
 }
 
+// NewOrphanSessionCheckWithSessionLister creates a check with a custom session lister (for testing).
+func NewOrphanSessionCheckWithSessionLister(lister SessionLister) *OrphanSessionCheck {
+	check := NewOrphanSessionCheck()
+	check.sessionLister = lister
+	return check
+}
+
 // Run checks for orphaned Gas Town tmux sessions.
 func (c *OrphanSessionCheck) Run(ctx *CheckContext) *CheckResult {
-	t := tmux.NewTmux()
+	lister := c.sessionLister
+	if lister == nil {
+		lister = &realSessionLister{t: tmux.NewTmux()}
+	}
 
-	sessions, err := t.ListSessions()
+	sessions, err := lister.ListSessions()
 	if err != nil {
 		return &CheckResult{
 			Name:    c.Name(),