Replace Web Push and its service worker with page notifications over SSE

web/src/state.ts

@@ -1,4 +1,5 @@
 import { get, put, subscribe, type AgentSession, type ByreEvent, type Focus, type InboxItem, type Project, type Snapshot, type Task, type TaskTab, type User } from "./api.js";
+import { notifyInbox } from "./notifications.js";
 
 export type Topic =
   | "me"
@@ -316,6 +317,9 @@ export function handleEvent(ev: ByreEvent): void {
       }
       break;
     case "inbox.created":
+      notifyInbox(ev.payload as unknown as InboxItem);
+      void loadInbox();
+      break;
     case "inbox.updated":
       void loadInbox();
       break;