Map the Frame controllers' buttons; make gaze clicks correctable

The Frame controllers aren't input devices on the host, so the pointer
helper reads them with SteamVR input (vrbuttons.h, actions/), one action
set per button, and sends presses to the relay, which does the mapped
action like for a mouse button. Only mapped buttons are taken, at an
overlay-global priority (SteamVR's experimental "Enable global input from
overlays"), and only outside games unless In games is on. Frametop Input
Settings gets a Controllers page to map them.

Gaze mode: a left press while the gaze has the pointer isn't sent at
once. The pointer stops, you drag it onto what you meant with the button
held, and the release clicks there; a press held still for
POINTER_GAZE_HOLD (0.5 s) becomes a real press, for drags. The dot shows
only while the mouse moves it (POINTER_GAZE_SHOW), while a press is held,
and as a pulse per click. Outside games the pointer stays on while gaze
mode is on. ft-gazed takes a third of each lesson's offset instead of all
of it: in the first live test one 6 degree lesson moved everything and put
the next target 7 degrees off. Frametop Input Settings gets a Gaze page.

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

docs/reference.md

@@ -98,15 +98,17 @@ pointer/helper/run.sh status | log | restart
 pointer/driver/install.sh probe     # devices, hand roles, who owns the dashboard pointer
 ```
 
-The pointer settings are in `~/.config/frametop.conf`: `POINTER_SENSITIVITY`, `POINTER_IDLE`, `POINTER_WAKE_COUNTS`, `POINTER_DISTANCE`, `POINTER_CURSOR_DEG`, `POINTER_ORIGIN_FRACTION`, `POINTER_ORIGIN_MARGIN`, `POINTER_SCENE_RADIUS`, `POINTER_EDGE_REACH`, `POINTER_LASER_WIDTH`, the head follow settings `POINTER_FOLLOW`, `POINTER_LEASH_DEG`, `POINTER_LEASH_DELAY`, `POINTER_LEASH_RETURN`, and `POINTER_FOLLOW_REACH`, and the gaze mode settings `POINTER_GAZE`, `POINTER_GAZE_RETAKE`, and `POINTER_GAZE_NUDGE_MAX`. The example config explains each. Frametop Input Settings changes them live; after editing the file by hand, restart the relay or the helper.
+The pointer settings are in `~/.config/frametop.conf`: `POINTER_SENSITIVITY`, `POINTER_IDLE`, `POINTER_WAKE_COUNTS`, `POINTER_DISTANCE`, `POINTER_CURSOR_DEG`, `POINTER_ORIGIN_FRACTION`, `POINTER_ORIGIN_MARGIN`, `POINTER_SCENE_RADIUS`, `POINTER_EDGE_REACH`, `POINTER_LASER_WIDTH`, the head follow settings `POINTER_FOLLOW`, `POINTER_LEASH_DEG`, `POINTER_LEASH_DELAY`, `POINTER_LEASH_RETURN`, and `POINTER_FOLLOW_REACH`, and the gaze mode settings `POINTER_GAZE`, `POINTER_GAZE_RETAKE`, `POINTER_GAZE_NUDGE_MAX`, `POINTER_GAZE_HOLD`, and `POINTER_GAZE_SHOW`. The example config explains each. Frametop Input Settings changes them live; after editing the file by hand, restart the relay or the helper.
 
 ## Frametop Input Settings
 
-A Kirigami app with a Python backend, in the Plasma menu under Settings. It runs in the `dev` container and talks to the relay over its control socket, `@frametop_relay`. It has four pages:
+A Kirigami app with a Python backend, in the Plasma menu under Settings. It runs in the `dev` container and talks to the relay over its control socket, `@frametop_relay`. It has six pages:
 
 - Devices lists every USB and Bluetooth mouse and keyboard, with a light that flashes when the device is used. Each device gets a role: 3D pointer (grabbed, drives the pointer; the default for anything with a mouse), Pass through (grabbed only while typing goes to the desktop; the default for keyboards, where a Meta tap toggles the dashboard if `META_DASHBOARD=1` is in `~/.config/frametop.conf`), or Ignore. A device is identified by its Bluetooth address, or its USB ids and name, so all of its input nodes share one role. Forget drops everything saved for a device.
 - Buttons maps a pointer device's buttons. Choose Capture a button, press the button or key, then pick an action: a click, back, scroll, toggle dashboard, recenter, pointer on or off, head follow on or off, gaze pointer on or off, faster or slower, pass the key through, or nothing. Devices with saved mappings are listed even while they're asleep.
+- Controllers maps the Frame controllers' buttons (every button but the system button) to the same actions, except passing a key through. Capture a button and press it on a controller, or pick it from the list. The controllers aren't input devices on the host; only SteamVR sees them. So the pointer helper reads them with SteamVR input (`pointer/helper/vrbuttons.h`, `pointer/helper/actions/`) and sends presses to the relay (`vrbtn right/a 1`), which does the mapped action. The helper only takes the buttons that are mapped (the relay tells it with `vrbind`), at an overlay-global priority, and only while no game (scene application) runs, so games keep every button; with In games on (`controller_in_games`), a mapped button is taken from games too. That needs SteamVR's "Enable global input from overlays (Experimental)" setting (`steamvr/globalActionSetPriority`); the page offers to turn it on. Mappings are saved as `controller_buttons` in `~/.config/frametop-input.json`.
 - Pointer has a Head follow switch and sliders for the pointer settings, which apply immediately, and a Recenter button.
+- Gaze has the gaze pointer switch (on now and from now on; a mapped button toggles it until the helper restarts), the gaze mode sliders, the gaze service's state (headset, samples per second, whether only one eye is tracked, the calibration, the nudges learned), and Calibrate (opens the gaze probe), Reload calibration, and Forget nudges.
 - Bluetooth lists paired devices and has Apply Bluetooth fixes, which runs `/etc/steamframe/bt-fixups.sh` through `pkexec`. Pair new devices in Steam.
 
 Device rules are saved in `~/.config/frametop-input.json`. `input-settings/install.sh` installs the menu entry. Its launcher hands podman the real `XDG_RUNTIME_DIR` and user bus and gives the app the session's Wayland socket, because the desktop session runs on a private D-Bus and podman fails on it.