fix(dog): properly set identity for dog sessions

Three fixes to make dog dispatch work end-to-end:

1. Add BuildDogStartupCommand in loader.go
   - Similar to BuildPolecatStartupCommand/BuildCrewStartupCommand
   - Passes AgentName to AgentEnv so BD_ACTOR is exported in startup command

2. Use BuildDogStartupCommand in dog.go
   - Removes ineffective SetEnvironment calls (env vars set after shell starts
     don't propagate to already-running processes)

3. Add "dog" case in mail_identity.go detectSenderFromRole
   - Dogs now use BD_ACTOR for mail identity
   - Without this, dogs fell through to "overseer" and couldn't find their mail

Tested: dog alpha now correctly sees inbox as deacon/dogs/alpha

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

internal/cmd/dog.go

@@ -852,8 +852,9 @@ func runDogDispatch(cmd *cobra.Command, args []string) error {
 	}
 
 	// Build startup command with initial prompt to check mail and execute plugin
+	// Use BuildDogStartupCommand to properly set BD_ACTOR=deacon/dogs/<name> in the startup command
 	initialPrompt := fmt.Sprintf("I am dog %s. Check my mail inbox with 'gt mail inbox' and execute the plugin instructions I received.", targetDog.Name)
-	startCmd := config.BuildAgentStartupCommand("dog", "", townRoot, targetDog.Path, initialPrompt)
+	startCmd := config.BuildDogStartupCommand(targetDog.Name, townRoot, targetDog.Path, initialPrompt)
 
 	// Create session from dog's directory
 	if err := t.NewSessionWithCommand(dogSessionName, targetDog.Path, startCmd); err != nil {
@@ -862,16 +863,6 @@ func runDogDispatch(cmd *cobra.Command, args []string) error {
 		}
 		// Non-fatal: mail was sent, dog is marked as working, but no session to execute
 		// The deacon or human can manually start the session later
-	} else {
-		// Set environment for the dog session
-		envVars := config.AgentEnv(config.AgentEnvConfig{
-			Role:      "dog",
-			AgentName: targetDog.Name,
-			TownRoot:  townRoot,
-		})
-		for k, v := range envVars {
-			_ = t.SetEnvironment(dogSessionName, k, v)
-		}
 	}
 
 	// Success - output result

internal/cmd/mail_identity.go

@@ -129,6 +129,13 @@ func detectSenderFromRole(role string) string {
 			return fmt.Sprintf("%s/refinery", rig)
 		}
 		return detectSenderFromCwd()
+	case "dog":
+		// Dogs use BD_ACTOR directly (set by BuildDogStartupCommand)
+		actor := os.Getenv("BD_ACTOR")
+		if actor != "" {
+			return actor
+		}
+		return detectSenderFromCwd()
 	default:
 		// Unknown role, try cwd detection
 		return detectSenderFromCwd()

internal/config/loader.go

@@ -1457,6 +1457,17 @@ func BuildPolecatStartupCommandWithAgentOverride(rigName, polecatName, rigPath,
 	return BuildStartupCommandWithAgentOverride(envVars, rigPath, prompt, agentOverride)
 }
 
+// BuildDogStartupCommand builds the startup command for a deacon dog.
+// Sets GT_ROLE, BD_ACTOR, GIT_AUTHOR_NAME, and GT_ROOT.
+func BuildDogStartupCommand(dogName, townRoot, dogPath, prompt string) string {
+	envVars := AgentEnv(AgentEnvConfig{
+		Role:      "dog",
+		AgentName: dogName,
+		TownRoot:  townRoot,
+	})
+	return BuildStartupCommand(envVars, dogPath, prompt)
+}
+
 // BuildCrewStartupCommand builds the startup command for a crew member.
 // Sets GT_ROLE, GT_RIG, GT_CREW, BD_ACTOR, GIT_AUTHOR_NAME, and GT_ROOT.
 func BuildCrewStartupCommand(rigName, crewName, rigPath, prompt string) string {