fix: final review wave — public routes, inbox 419, url schemes, deep_link, tests

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BCrwHHnGCB5XH968Nxokqw

core/tests/Feature/SchemaTest.php

@@ -110,5 +110,6 @@ class SchemaTest extends TestCase
         $this->assertTrue(EventState::Overdue->countsInBadge());
         $this->assertFalse(EventState::Preparing->countsInBadge());
         $this->assertSame(['scheduled', 'preparing', 'today', 'overdue'], EventState::nonTerminalValues());
+        $this->assertSame(['today', 'overdue'], EventState::badgeValues());
     }
 }