feat(admin): show email count and last-email date per feed

Surface each feed's email count on its Emails button and a "Last email …"
freshness line under the title, in both dashboard views. The values are
projected into feeds:list (kept to a single KV read) via the Feed aggregate,
so toListItemDTO now maps the whole aggregate through its intention-revealing
accessors instead of threading scalar projections. Also fixes long titles
overflowing into the Feed ID column in the table view.

Co-Authored-By: Claude Opus 4.7 <[email protected]>

src/domain/feed.aggregate.test.ts

@@ -200,6 +200,34 @@ describe("Feed.removeEmails", () => {
   });
 });
 
+describe("Feed.emailCount / lastEmailAt", () => {
+  it("reports zero and undefined for an empty feed", () => {
+    const feed = Feed.reconstitute(FID, state(), { emails: [] });
+    expect(feed.emailCount).toBe(0);
+    expect(feed.lastEmailAt).toBeUndefined();
+  });
+
+  it("counts emails and reports the newest receivedAt (index head)", () => {
+    const feed = Feed.reconstitute(FID, state(), {
+      emails: [
+        entry({ key: "k2", receivedAt: 2000 }),
+        entry({ key: "k1", receivedAt: 1000 }),
+      ],
+    });
+    expect(feed.emailCount).toBe(2);
+    expect(feed.lastEmailAt).toBe(2000);
+  });
+
+  it("tracks the latest email after ingest", () => {
+    const feed = Feed.reconstitute(FID, state(), {
+      emails: [entry({ key: "old", receivedAt: 1000 })],
+    });
+    feed.ingest(entry({ key: "new", receivedAt: 5000 }), { maxBytes: 10_000 });
+    expect(feed.emailCount).toBe(2);
+    expect(feed.lastEmailAt).toBe(5000);
+  });
+});
+
 describe("Feed events", () => {
   it("records FeedCreated on create and drains it once", () => {
     const feed = Feed.create(FID, createInput(), { mailboxId: MBOX });
@@ -333,6 +361,27 @@ describe("FeedRepository.load / save round-trip", () => {
     ]);
   });
 
+  it("projects email count and last-email timestamp into feeds:list", async () => {
+    const repo = new FeedRepository(mockEnv().EMAIL_STORAGE);
+    const created = Feed.create(FID, createInput({ title: "Proj" }), {
+      mailboxId: MBOX,
+    });
+    await repo.save(created);
+
+    let listed = await repo.listFeeds();
+    expect(listed[0].emailCount).toBe(0);
+    expect(listed[0].lastEmailAt).toBeUndefined();
+
+    created.ingest(entry({ key: "feed:opaque-feed-id:1", receivedAt: 4242 }), {
+      maxBytes: 1_000_000,
+    });
+    await repo.saveMetadata(created);
+
+    listed = await repo.listFeeds();
+    expect(listed[0].emailCount).toBe(1);
+    expect(listed[0].lastEmailAt).toBe(4242);
+  });
+
   it("returns null when the feed has no config", async () => {
     const repo = new FeedRepository(mockEnv().EMAIL_STORAGE);
     expect(await repo.load(FeedId.unchecked("missing"))).toBeNull();