Gaze: idle while the gaze isn't used

The gaze service ran ft-gaze and our own eye tracker all the time: with gaze mode off, ft-eyes
still took about 60% of a core, and ft-eyegrab, ft-gaze and ft-gazed 3 to 4% each. Now ft-gaze
and our tracker run only while gaze mode is on and someone wears the headset, while a check or
the calibration is open or asked for, or under a "wake" lease, which the Gaze page of Frametop
Input Settings renews while it's open. 30 s after the last use they stop, and the frame grabber
idles with our tracker.

- The pointer helper answers "gaze ? headset" with worn|away (SteamVR's activity level for the
  headset); an older helper answers it as before, and the service then goes by gaze mode alone.
- A quick check, calibration, or fit check asked for while idle wakes the tracker and opens once
  it sends; the automatic calibration waits quietly while it starts.
- Status has "awake" and "idle" (why), and the Gaze page shows it.
- gaze/test/idle-test.py runs the service with a fake helper and ft-gaze, offline.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/design.md

@@ -191,7 +191,7 @@ Staying awake while charging uses Steam's own setting rather than a logind sleep
 
 ## Pausing for VR games
 
-Hiding the screens during a game kept them out of view, but Frametop kept using the headset. Measured on 2026-10-02 with gaze mode off and no game running, in shares of one core: our eye tracker (ft-eyes) about 60%, ft-eyegrab, ft-gaze and ft-gazed about 3 to 4% each; remote desktop (krdpserver, FreeRDP, Xvnc) about 2 cores while it ran; KWin about 13%, ft-screens about 4%. The gaze service runs at full rate whether gaze mode is on or not. Reading SteamVR's eye tracking 90 times a second also made it restart every 10 to 13 seconds during Beat Saber, and each restart took input focus from the game, which paused it (PR #13; since then ft-gaze skips SteamVR's gaze action during games, but our own tracker kept running). So pausing stops what costs the most and leaves windows where they are.
+Hiding the screens during a game kept them out of view, but Frametop kept using the headset. Measured on 2026-10-02 with gaze mode off and no game running, in shares of one core: our eye tracker (ft-eyes) about 60%, ft-eyegrab, ft-gaze and ft-gazed about 3 to 4% each; remote desktop (krdpserver, FreeRDP, Xvnc) about 2 cores while it ran; KWin about 13%, ft-screens about 4%. The gaze service ran at full rate whether gaze mode was on or not; now it idles while the gaze isn't used (gaze/README.md), and pausing stops it outright. Reading SteamVR's eye tracking 90 times a second also made it restart every 10 to 13 seconds during Beat Saber, and each restart took input focus from the game, which paused it (PR #13; since then ft-gaze skips SteamVR's gaze action during games, but our own tracker kept running). So pausing stops what costs the most and leaves windows where they are.
 
 - A hidden screen still cost as much as a visible one. ft-screens sent every committed screen its frame callback at 90 Hz whether its overlay showed or not, so KWin kept drawing, and its apps with it. Paused, ft-screens sends the callbacks once a second. A Wayland client draws again only after its last frame's callback, so KWin's output stalls, KWin's own clients stop getting theirs, and the whole desktop idles, without anything losing its connection. A second's pace, rather than none, keeps any client that waits on a callback from waiting forever. Stopping KWin or the apps with SIGSTOP would free the same, but a Wayland peer that stops reading overflows the other side's 4 KB socket buffer, which ends the connection: that's how the live desktop died once when its KWin stalled (`Data too big for buffer`). They also sit in different cgroups (KWin under steam.service when the VR launcher starts it, ft-screens in the dev container's), so no single freeze stops them together.
 - The relay does the pausing because it's the one part that always runs, and the pointer helper keeps running because stopping it leaves its virtual controller connected with its last pose (the driver has no staleness timeout), maybe holding a hand role, with the 3D mouse dead. Releasing it does the job. The helper already checks for a scene app twice a second, so it's what tells the relay a game started.