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.

booth/app.py

@@ -171,6 +171,7 @@ def set_blurred(booth: Path, rel: str, on: bool) -> set[str]:
 # can use it without pulling FastAPI in. Re-exported here because call sites and
 # tests already reference these names through app.
 from booth.thumbs import THUMB_DIR, ensure_thumb
+from booth.birthtime import birth_time
 from booth.asks import (  # noqa: E402
     ANSWER_SUFFIX,
     ASK_SUFFIX,
@@ -706,6 +707,16 @@ def list_booths(data_dir: Path, ttl_seconds: float, now: float | None = None) ->
                 # `landed_at` is content. "New since you looked" reads only the
                 # second, so a flag or a view never makes a booth look new.
                 "landed_at": _content_mtime(child),
+                # WHEN THE BOOTH WAS MADE, from the filesystem's own record.
+                # ONE RULE for all thirty: `.booth.json`'s declared `created`
+                # only exists for booths posted through the CLI since U5, and
+                # twelve 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, and
+                # directory mtime just means "last thing added". ext4 records a
+                # real birth time; this reads it. None when the filesystem
+                # cannot say, and None renders as nothing.
+                "created_at": birth_time(child),
                 "viewed_at": _viewed_at(child),
                 # The first four images in item order, as the originals shown
                 # small. Blurred ones stay blurred, the cover's rule.
@@ -1263,6 +1274,10 @@ def create_app(
                 # a booth URL handed to the operator lands HERE, never on the
                 # index, and job 5 is "operator, look at this".
                 "manifest": read_manifest(booth),
+                # Same two clocks the Desk row carries, because a booth URL
+                # handed to the operator lands HERE and not on the index.
+                "created_at": birth_time(booth),
+                "landed_at": _content_mtime(booth),
                 # The lifetime line, same three states as the index card: a
                 # booth URL handed to the operator lands HERE, not on the index,
                 # so "why is this not counting down" has to be answerable here.