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_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 ":"
 		},