fix(input): pointer lock + the missing per-iteration motion flush

Two capture bugs compounding into 'sluggish and not captured':

1. flush_motion was never called from the run loop — the GTK client's
   frame-clock tick flushed pending motion every frame, and the port
   lost it. Pure mouse movement only reached the host when a click/key/
   scroll happened to flush it; the host cursor simply didn't follow.
   Now one coalesced MouseMove per loop iteration.

2. Capture forwarded ABSOLUTE letterboxed coordinates with no pointer
   confinement (GTK parity, the plan's deferred 'stage-2' item): the
   visible local cursor outran the host cursor by the full e2e and
   escaped the window. Capture is now real pointer lock — SDL relative
   mouse mode (hidden, confined, raw deltas) with relative MouseMove on
   the wire, so the host cursor is the only cursor.

Also: focus-gain re-engages after an auto-release (Alt-Tab undoes
itself; the startup focus race can no longer strand the session
uncaptured) while a chord release stays released until the user opts
back in.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

crates/punktfunk-host/src/vdisplay/linux/gamescope.rs

@@ -987,7 +987,10 @@ fn do_restore_tv_session() {
             use super::ActiveKind;
             if matches!(
                 super::detect_active_session().kind,
-                ActiveKind::DesktopKde | ActiveKind::DesktopGnome | ActiveKind::DesktopWlroots
+                ActiveKind::DesktopKde
+                    | ActiveKind::DesktopGnome
+                    | ActiveKind::DesktopWlroots
+                    | ActiveKind::DesktopHyprland
             ) {
                 tracing::info!(
                     "gamescope (SteamOS): a desktop session is active — removed the headless \