Add contact form with reCAPTCHA, saved to DB, viewable in admin

Adds a public /contact page (name/email/message, protected by the same
reCAPTCHA v3 setup used on registration) that persists submissions to
a new contact_message table, plus a Contact section in the admin panel
to read them. Linked from the site footer.

templates/game/admin/base.html.twig

@@ -136,6 +136,7 @@
                 { route: 'game_admin_games',     label: 'Games',      icon: '🎮' },
                 { route: 'game_admin_sessions',  label: 'Sessions',   icon: '▶' },
                 { route: 'game_admin_feedback',  label: 'Feedback',   icon: '💬' },
+                { route: 'game_admin_contact',   label: 'Contact',    icon: '📨' },
                 { route: 'game_admin_email_log', label: 'Email Log',  icon: '✉' },
             ] %}