Pause gesture: look the controllers up every 30 s, not every 3 s

The gesture reader fetched vrserver's /input/getstate.json over HTTP every 3 seconds, the
whole time the relay runs, to notice a controller's root path changing when the 3D mouse
takes or gives back its hand role.

It now looks them up when it connects, when a message comes from a device path it doesn't
know (at most every 3 s; the device is read from the message with two string searches, not
a JSON parse of all 160 a second), 1.5 s after the relay's 3D mouse connects or lets go (the
relay tells it through GamePause.controllers_changed), and otherwise every 30 s. The keys
test's pause stub gets the new method.

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

docs/design.md

@@ -197,7 +197,7 @@ Hiding the screens during a game kept them out of view, but Frametop kept using
 
 - 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.
-- The gesture has to work during a game, but SteamVR input reaches only the app with input focus, and an overlay with global input (`steamvr/globalActionSetPriority`) takes the buttons it binds from the game. vrserver's web socket on 127.0.0.1:27062, which its controller binding page uses for the live view, reports every controller component whatever has focus, and reading it takes nothing. The game sees the clicks too, so the default is a gesture games hardly use: both thumbsticks, together, twice. "Together" means within 0.3 seconds of each other, so a stick held down to sprint while the other clicks doesn't count. The stream is about 160 messages a second, nearly all capacitive sensing, so the reader parses only the few that mention a gesture's button. A controller's root path changes while the 3D mouse holds its hand role (`/devices/cv/<serial>` instead of `/user/hand/right`), so the reader looks the controllers up again every 3 seconds.
+- The gesture has to work during a game, but SteamVR input reaches only the app with input focus, and an overlay with global input (`steamvr/globalActionSetPriority`) takes the buttons it binds from the game. vrserver's web socket on 127.0.0.1:27062, which its controller binding page uses for the live view, reports every controller component whatever has focus, and reading it takes nothing. The game sees the clicks too, so the default is a gesture games hardly use: both thumbsticks, together, twice. "Together" means within 0.3 seconds of each other, so a stick held down to sprint while the other clicks doesn't count. The stream is about 160 messages a second, nearly all capacitive sensing, so the reader parses only the few that mention a gesture's button. A controller's root path changes while the 3D mouse holds its hand role (`/devices/cv/<serial>` instead of `/user/hand/right`), so the reader looks the controllers up again (an HTTP request to vrserver): when the relay's 3D mouse connects or lets go, when a message comes from a device it doesn't know, and every 30 seconds. It used to be every 3 seconds.
 - Resuming starts remote desktop through `systemd-run --scope`: started straight from the relay, it would join the relay's cgroup and end with the next relay restart.
 
 ## SteamOS updates