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/inject.rs

@@ -149,7 +149,12 @@ pub fn default_backend() -> Backend {
             if c.eq_ignore_ascii_case("kwin") {
                 return Backend::KwinFakeInput;
             }
-            if c.eq_ignore_ascii_case("wlroots") || c.eq_ignore_ascii_case("sway") {
+            if c.eq_ignore_ascii_case("wlroots")
+                || c.eq_ignore_ascii_case("sway")
+                // Hyprland kept the wlr virtual-input protocols, so it injects through the same
+                // backend as sway/river (design/hyprland-support.md D4).
+                || c.eq_ignore_ascii_case("hyprland")
+            {
                 return Backend::WlrVirtual;
             }
             // mutter (GNOME) falls through to the XDG_CURRENT_DESKTOP check below.