feat: add RoleEnvVars and improve gt role CLI

Introduces config.RoleEnvVars() as the single source of truth for role
identity environment variables (GT_ROLE, GT_RIG, BD_ACTOR, etc.).

CLI improvements:
- Fix getRoleHome paths (witness has no /rig suffix, polecat/crew do)
- Make gt role env read-only (displays current role from env/cwd)
- Add EnvIncomplete handling: fill missing env vars from cwd with warning
- Add cwd mismatch warnings when not in role home directory
- gt role home now validates --polecat requires --rig

Includes comprehensive e2e tests for all role detection scenarios.

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

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

internal/config/loader.go

@@ -1170,6 +1170,46 @@ func BuildStartupCommandWithAgentOverride(envVars map[string]string, rigPath, pr
 	return cmd, nil
 }
 
+// RoleEnvVars returns the canonical environment variables for a role.
+// This is the single source of truth for role identity env vars.
+// The role parameter should be one of: "mayor", "deacon", "witness", "refinery", "polecat", "crew".
+// For rig-specific roles, rig must be provided.
+// For polecat/crew, polecatOrCrew must be the polecat or crew member name.
+func RoleEnvVars(role, rig, polecatOrCrew string) map[string]string {
+	envVars := map[string]string{
+		"GT_ROLE": role,
+	}
+
+	switch role {
+	case "mayor":
+		envVars["BD_ACTOR"] = "mayor"
+		envVars["GIT_AUTHOR_NAME"] = "mayor"
+	case "deacon":
+		envVars["BD_ACTOR"] = "deacon"
+		envVars["GIT_AUTHOR_NAME"] = "deacon"
+	case "witness":
+		envVars["GT_RIG"] = rig
+		envVars["BD_ACTOR"] = fmt.Sprintf("%s/witness", rig)
+		envVars["GIT_AUTHOR_NAME"] = fmt.Sprintf("%s/witness", rig)
+	case "refinery":
+		envVars["GT_RIG"] = rig
+		envVars["BD_ACTOR"] = fmt.Sprintf("%s/refinery", rig)
+		envVars["GIT_AUTHOR_NAME"] = fmt.Sprintf("%s/refinery", rig)
+	case "polecat":
+		envVars["GT_RIG"] = rig
+		envVars["GT_POLECAT"] = polecatOrCrew
+		envVars["BD_ACTOR"] = fmt.Sprintf("%s/polecats/%s", rig, polecatOrCrew)
+		envVars["GIT_AUTHOR_NAME"] = polecatOrCrew
+	case "crew":
+		envVars["GT_RIG"] = rig
+		envVars["GT_CREW"] = polecatOrCrew
+		envVars["BD_ACTOR"] = fmt.Sprintf("%s/crew/%s", rig, polecatOrCrew)
+		envVars["GIT_AUTHOR_NAME"] = polecatOrCrew
+	}
+
+	return envVars
+}
+
 // BuildAgentStartupCommand is a convenience function for starting agent sessions.
 // It sets standard environment variables (GT_ROLE, BD_ACTOR, GIT_AUTHOR_NAME)
 // and builds the full startup command.