feat(config): set GT_ROOT env var for all agent sessions

Previously GT_ROOT was documented as a formula search path but never
actually set, making $GT_ROOT/.beads/formulas/ unreachable for agents.

Now BuildStartupCommand automatically sets GT_ROOT to the town root,
enabling all agents (witness, refinery, polecat, crew, etc.) to find
town-level formulas without relying on cwd-relative paths.

Also adds a doctor check (gt-root-env) that warns when existing sessions
are missing GT_ROOT, with instructions to restart sessions.

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

internal/config/loader.go

@@ -1064,13 +1064,15 @@ func findTownRootFromCwd() (string, error) {
 // prompt is optional - if provided, appended as the initial prompt.
 func BuildStartupCommand(envVars map[string]string, rigPath, prompt string) string {
 	var rc *RuntimeConfig
+	var townRoot string
 	if rigPath != "" {
 		// Derive town root from rig path
-		townRoot := filepath.Dir(rigPath)
+		townRoot = filepath.Dir(rigPath)
 		rc = ResolveAgentConfig(townRoot, rigPath)
 	} else {
 		// Try to detect town root from cwd for town-level agents (mayor, deacon)
-		townRoot, err := findTownRootFromCwd()
+		var err error
+		townRoot, err = findTownRootFromCwd()
 		if err != nil {
 			rc = DefaultRuntimeConfig()
 		} else {
@@ -1078,6 +1080,11 @@ func BuildStartupCommand(envVars map[string]string, rigPath, prompt string) stri
 		}
 	}
 
+	// Add GT_ROOT so agents can find town-level resources (formulas, etc.)
+	if townRoot != "" {
+		envVars["GT_ROOT"] = townRoot
+	}
+
 	// Build environment export prefix
 	var exports []string
 	for k, v := range envVars {