Conversations page, and know what is unread

/api/v1/conversations answered one page, never unread, its read endpoint
did nothing, and DELETE was missing; each conversation cost a query per
member. Now each conversation keeps its newest post (DmGroup.LastPostId,
set as posts arrive, learnt once by migration _013) and pages by it as
Mastodon does, and each persona's ConversationState holds what it read and
what it took off its list:

- unread when someone else wrote last, after what the persona read;
- read marks it so, and writing in a conversation reads it;
- DELETE takes it off the list until a newer message brings it back.

The list reads its states, newest posts, members and accounts in a few
queries per page.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LsXgEaXee4GCU1hwYgPJXw

PrivaPub.Tests/Http/MastodonTimelinesTests.cs

@@ -146,6 +146,43 @@ namespace PrivaPub.Tests.Http
 			Assert.DoesNotContain(answer, (await stranger.Client.Get($"/api/v1/accounts/{bob.Id}/statuses")).Ok().Ids);
 		}
 
+		[Fact]
+		public async Task Conversations_page_by_their_newest_message_and_know_what_is_unread_read_and_removed()
+		{
+			var alice = await _host.Mastodon("alice");
+			var bob = await _host.Mastodon("bob");
+			var carol = await _host.Mastodon("carol");
+			await bob.Status($"@{alice.UserName} first", ("visibility", "direct"));
+			var fromCarol = (await carol.Status($"@{alice.UserName} second", ("visibility", "direct"))).Text("id");
+			// writing in a conversation reads it
+			await alice.Status($"@{bob.UserName} third", ("visibility", "direct"));
+			async Task<JsonArray> List() => (await alice.Client.Get("/api/v1/conversations")).Ok().Array;
+
+			var all = await List();
+			Assert.Equal(2, all.Count);
+			var (withBob, withCarol) = (all[0].Text("id"), all[1].Text("id"));
+			Assert.Equal(new[] { bob.Id }, all[0]!["accounts"]!.AsArray().Select(a => a.Text("id")));
+			Assert.False(all[0].Flag("unread"));
+			Assert.True(all[1].Flag("unread"));
+			Assert.Equal(fromCarol, all[1]!["last_status"].Text("id"));
+
+			var page = (await alice.Client.Get("/api/v1/conversations?limit=1")).Ok();
+			Assert.Equal(withBob, Assert.Single(page.Array).Text("id"));
+			Assert.Equal(withCarol, Assert.Single((await alice.Client.Get(page.Link("next"))).Ok().Array).Text("id"));
+
+			Assert.False((await alice.Client.Post($"/api/v1/conversations/{withCarol}/read")).Ok().Body.Flag("unread"));
+			Assert.False((await List()).Single(c => c.Text("id") == withCarol).Flag("unread"));
+
+			// off the list until a newer message, which brings it back unread; carol's own list never changed
+			(await alice.Client.Delete($"/api/v1/conversations/{withCarol}")).Ok();
+			Assert.Equal(new[] { withBob }, (await List()).Select(c => c.Text("id")));
+			Assert.Equal(withCarol, Assert.Single((await carol.Client.Get("/api/v1/conversations")).Ok().Array).Text("id"));
+			var again = (await carol.Status($"@{alice.UserName} are you there?", ("visibility", "direct"))).Text("id");
+			var back = (await List())[0];
+			Assert.Equal((withCarol, again, true), (back.Text("id"), back!["last_status"].Text("id"), back.Flag("unread")));
+			Assert.Equal(HttpStatusCode.NotFound, (await bob.Client.Delete($"/api/v1/conversations/{withCarol}")).Status);
+		}
+
 		[Fact]
 		public async Task Markers_are_saved_versioned_and_read_back_per_timeline()
 		{