fix(mayor): match handoff priming for gt may at startup (hq-osbot)

When starting Mayor via 'gt may at', the session now:
1. Works from townRoot (~/gt) instead of mayorDir (~/gt/mayor)
2. Includes startup beacon with explicit instructions in initial prompt
3. Removes redundant post-start nudges (beacon has instructions)

This matches the 'gt handoff' behavior where the agent immediately
knows to check hook and mail on startup.

Fixes: hq-h3449 (P0 escalation - horrendous starting UX)

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

internal/session/startup.go

@@ -65,9 +65,9 @@ func FormatStartupNudge(cfg StartupNudgeConfig) string {
 	beacon := fmt.Sprintf("[GAS TOWN] %s <- %s • %s • %s",
 		cfg.Recipient, cfg.Sender, timestamp, topic)
 
-	// For handoff, add explicit instructions so the agent knows what to do
+	// For handoff and cold-start, add explicit instructions so the agent knows what to do
 	// even if hooks haven't loaded CLAUDE.md yet
-	if cfg.Topic == "handoff" {
+	if cfg.Topic == "handoff" || cfg.Topic == "cold-start" {
 		beacon += "\n\nCheck your hook and mail, then act on the hook if present:\n" +
 			"1. `gt hook` - shows hooked work (if any)\n" +
 			"2. `gt mail inbox` - check for messages\n" +

internal/session/startup_test.go

@@ -41,6 +41,9 @@ func TestFormatStartupNudge(t *testing.T) {
 				"deacon",
 				"<- mayor",
 				"cold-start",
+				"Check your hook and mail", // cold-start includes explicit instructions (like handoff)
+				"gt hook",
+				"gt mail inbox",
 			},
 			// No wantNot - timestamp contains ":"
 		},