feat: TUI room creation + daemon-side room persistence

/room <name> in the TUI sends create_room to the daemon, which persists
it in the rooms SQLite table and echoes room_created back. state_snapshot
now includes persisted rooms so they survive reconnects. Tab navigation
and room rendering pick them up automatically.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

internal/store/store.go

@@ -28,6 +28,11 @@ CREATE TABLE IF NOT EXISTS peers (
     alias       TEXT NOT NULL,
     last_seen   DATETIME NOT NULL
 );
+
+CREATE TABLE IF NOT EXISTS rooms (
+    name        TEXT PRIMARY KEY,
+    created_at  DATETIME NOT NULL
+);
 `
 
 // Store is a local SQLite-backed message and peer store.
@@ -119,6 +124,33 @@ func (s *Store) RecentMessages(room string, limit int) ([]proto.ChatMessage, err
 	return msgs, rows.Err()
 }
 
+// SaveRoom persists a room name. Duplicate names are silently ignored.
+func (s *Store) SaveRoom(name string) error {
+	_, err := s.db.Exec(
+		`INSERT OR IGNORE INTO rooms (name, created_at) VALUES (?, ?)`,
+		name, time.Now().UTC(),
+	)
+	return err
+}
+
+// Rooms returns all persisted room names, ordered by creation time.
+func (s *Store) Rooms() ([]string, error) {
+	rows, err := s.db.Query(`SELECT name FROM rooms ORDER BY created_at`)
+	if err != nil {
+		return nil, err
+	}
+	defer rows.Close()
+	var out []string
+	for rows.Next() {
+		var name string
+		if err := rows.Scan(&name); err != nil {
+			return nil, err
+		}
+		out = append(out, name)
+	}
+	return out, rows.Err()
+}
+
 // KnownPeers returns all peers seen since this daemon started storing data.
 func (s *Store) KnownPeers() (map[proto.PeerID]string, error) {
 	rows, err := s.db.Query(`SELECT peer_id, alias FROM peers`)