Input relay: send mouse motion at most every 4 ms

The relay sent the helper one "move" per SYN_REPORT, so a 1000 Hz mouse sent 1000 datagrams
a second to a helper whose loop runs every 8 ms, and each one went through a dozen sscanf
and strncmp tests in the helper before reaching the move handler. In a 200 ms test at
1000 Hz, 149 reports now make 45 moves with the same total.

flush() on a report now sends only once 4 ms have passed since the last move; tick() sends
the rest when due, and the select timeout shrinks to match. Buttons and the gaze
keys still flush first, unconditionally, so a click lands where the pointer was. In the
helper, "move" is now tested first in the command dispatch, and its handling is one lambda.

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

docs/design.md

@@ -153,7 +153,7 @@ SteamVR opens every input device only when it starts. When a Bluetooth mouse sle
 
 Keyboards aren't grabbed by default, because a grabbed keyboard's keys went into a virtual keyboard nothing typed from; the relay forwards them to ft-screens instead.
 
-The relay never waits on the pointer helper. Its socket to the helper used to block, so when the helper stalled (a layout placement or `grabprobe` holds it for seconds, and the gaze service fills its socket 90 times a second meanwhile), the whole relay stopped with it: keyboards, the volume keys, and pausing. Now what the helper doesn't take waits in order and goes out on the next loops. Mouse moves add up into one while they wait, and a scroll notch is dropped, since scrolling seconds late is no use; presses and releases are kept, so no button stays down.
+The relay never waits on the pointer helper. Its socket to the helper used to block, so when the helper stalled (a layout placement or `grabprobe` holds it for seconds, and the gaze service fills its socket 90 times a second meanwhile), the whole relay stopped with it: keyboards, the volume keys, and pausing. Now what the helper doesn't take waits in order and goes out on the next loops. Mouse moves add up into one while they wait, and a scroll notch is dropped, since scrolling seconds late is no use; presses and releases are kept, so no button stays down. Mouse motion goes to the helper at most every 4 ms, rather than once per report, which from a 1000 Hz mouse was 1000 datagrams a second to a helper that runs every 8 ms; a button sends the motion before it first, so the click lands where the pointer was.
 
 An ungrabbed keyboard reaches both sides at once. In VR, gamescope reads every input device itself (the SteamOS build's `InputStealer`, libinput with udev hotplug, so new devices too) and types into its focused app, and ft-screens types the same keys into the desktop. So Space in the desktop also paused Spotify on the dashboard. Typing now follows the last click. ft-screens sees clicks on its own screens, from the mouse or a controller. A click anywhere else is only visible for the mouse: overlay apps get SteamVR's `OverlayFocusChanged` (which panel the laser is on) but no controller button events, so the pointer helper reports the panel under the dot on each left press. ft-screens tells the relay where typing goes every second, from an unbound socket so the relay's replies can't loop back into its control socket, and the relay grabs pass-through keyboards while it's the desktop. A grab waits until the keyboard has no key down, so no key stays held on either side, and the relay lets go if ft-screens stops reporting. A program that reads every keyboard for a hotkey (a dictation tool, say) loses a grabbed keyboard. Repeating the keys on another input device doesn't work: gamescope reads that device too, whether it's the relay's virtual keyboard or one created later, and every Space, typed or dictated, paused Spotify again. So with `SHARE_KEYS=1` the relay sends a grabbed keyboard's keys to `@frametop_keys` as datagrams (`key <code> <value> <device name>`). It's off by default, because the relay can't tell who is listening: abstract sockets have no permissions, and any local process that binds the name first gets every key typed into the desktop, passwords included. A listener should accept only its own user (`SO_PASSCRED`) and skip any keyboard of its own that the relay grabs too.