feat(dates): creation and update times for every booth, from the filesystem

The operator: "I think I want creation and update dates on the booths now too."

UPDATE was already there — `landed_at`, the newest mtime among CONTENT
excluding our own machinery, which the Desk already sorts "new since you looked"
by.

CREATION had no honest source. `.booth.json` carries a declared `created`, but
only for booths posted through the CLI since U5 — TWELVE OF THIRTY live booths
had none. Every alternative was a guess wearing a fact's clothes: oldest content
mtime is wrong the moment an agent copies files with timestamps preserved;
directory mtime is just "last thing added", which is landed_at renamed; and
stamping a first-seen marker on read is the same write-on-read shape that spent
an hour of today aging the booth it cached.

ext4 records a real birth time. CPython does not expose st_birthtime on Linux,
so booth/birthtime.py reads it through statx(2) — a fact the disk already holds
rather than one we invent. Verified against stat(1) on live booths, 6 of 6
exact, including every booth with no manifest. ONE rule for all thirty, which is
what invariant 6 asks of anything statable in a line.

None when the filesystem cannot say (tmpfs, NFS, an old kernel), and None
renders as nothing — the honest output when nobody knows. Never raises:
list_booths calls it once per booth on every index load, so a read that can
raise is a service-wide outage wearing a single-booth bug's clothes.

ALSO TWO REAL TEST-HARNESS DEFECTS, found chasing a flake and fixed on their
merits rather than because they were proven to be the cause:

- The keyboard-flag browser test fired ArrowRight and `f` back to back,
  assuming the first had finished — and focus() does a scrollIntoView, so under
  load `f` could arrive with no cursor and flag nothing. It now waits for the
  cursor to land.
- BOTH browser fixtures did bind -> getsockname -> CLOSE -> hand uvicorn the
  port NUMBER, leaving a window for the kernel to give that port to somebody
  else. This suite runs two browser files that each start a server per test, so
  the competitor is right there. The bound socket is now handed over directly.

⚠ THE FLAKE IS NOT PROVEN FIXED. Two different browser tests failed once each
across full-suite runs while passing 3/3 and 5/5 in isolation; since the fixes,
one failure in three runs. n=3 cannot distinguish that from the prior rate and
this commit does not claim it does.

770 green on a clean run.

tests/test_booth.py

@@ -1726,3 +1726,55 @@ def test_the_blurbooth_route_toggles_and_lands_back(tmp_path):
 
     c.post("/b/g/blurbooth", data={"on": "0"}, follow_redirects=False)
     assert not (b / ".blurbooth").exists()
+
+
+def test_every_booth_can_state_when_it_was_made(tmp_path):
+    """The operator asked for creation dates. `.booth.json`'s declared
+    `created` only exists for booths posted through the CLI since U5 — twelve
+    of thirty live booths had none — and every alternative was a guess wearing
+    a fact's clothes: oldest content mtime is wrong the moment an agent copies
+    files with timestamps preserved, and directory mtime just means "last thing
+    added".
+
+    ext4 records a real birth time and `statx` reads it, so this is a FACT the
+    disk already holds. ONE rule for every booth, manifest or not.
+
+    Defeating change: falling back to `stat().st_mtime`, which changes every
+    time a file lands and would show a week-old booth as created five minutes
+    ago."""
+    import time
+
+    b = tmp_path / "g"
+    b.mkdir()
+    made = time.time()
+    (b / "a.png").write_bytes(b"x")
+
+    rows = {r["name"]: r for r in list_booths(tmp_path, ttl_seconds=86400)}
+    row = rows["g"]
+    assert row["created_at"] is not None, "no creation time for a fresh booth"
+    assert abs(row["created_at"] - made) < 10
+
+    # and it must NOT move when content lands later
+    time.sleep(1.1)
+    (b / "b.png").write_bytes(b"y")
+    again = {r["name"]: r for r in list_booths(tmp_path, ttl_seconds=86400)}["g"]
+    assert again["created_at"] == row["created_at"], \
+        "the creation time moved when a file was added — that is `updated`, not `created`"
+    assert again["landed_at"] > row["landed_at"], "`updated` did not move"
+
+
+def test_a_filesystem_with_no_birth_time_shows_nothing(tmp_path, monkeypatch):
+    """None renders as nothing, which is the honest output when nobody knows —
+    tmpfs, NFS and some overlayfs do not record a birth time, and an old kernel
+    has no `statx` at all.
+
+    Defeating change: substituting any mtime when birth_time returns None."""
+    import booth.app as app_mod
+
+    b = tmp_path / "g"
+    b.mkdir()
+    (b / "a.png").write_bytes(b"x")
+    monkeypatch.setattr(app_mod, "birth_time", lambda p: None)
+
+    row = {r["name"]: r for r in list_booths(tmp_path, ttl_seconds=86400)}["g"]
+    assert row["created_at"] is None