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/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 {