feat(clients/input): system buttons route around local overlays

Pressing guide/Steam/QAM collided with the client device's own shell: iOS 26
opens its Game Overlay for the Home press (no app opt-out until iOS 27 makes
it a user setting), and a Gaming-Mode client opened BOTH Steam overlays for
one press — the local one covering the stream.

Two cross-client tier-P settings, zero wire changes:

- system_buttons (auto|forward|local): raw guide+misc1 passthrough. Auto
  forwards everywhere EXCEPT under gamescope, where SteamOS reacts to the
  same physical press no matter what.
- guide_gesture (auto|on|off): hold Select ALONE ~350ms sends the HOST's
  guide, down until release — held on, that's the host's long-press, which
  opens a Gaming-Mode host's QAM for regular pads. A Select tap is delivered
  on release with its up TAP_PRESS (50ms) behind, because per-transition
  sends fold into seq'd GamepadState snapshots and a back-to-back pair can
  coalesce into no press at all. A Select inside a combo (the escape chord)
  passes through untouched. Auto arms it only where the raw press can't
  reach the host cleanly: gamescope, iOS/iPadOS, tvOS.

The same SelectGesture rules live in pf-client-core (pure state machine +
unit tests), the Apple client (mask-diff adaptation in GamepadCapture), and
Android's GamepadRouter. Settings rows on every surface (GTK, WinUI,
console UI, Decky, Apple x2, Android x2) with profile plumbing throughout.

punktfunk-session grows a control socket
($XDG_RUNTIME_DIR[/app/$FLATPAK_ID]/punktfunk-session-ctl.sock — the one
runtime path a flatpak and the host see identically): 'guide'/'qam' verbs
inject synthetic taps. The Decky panel gains a Host menus section (visible
while the client runs) whose buttons press the host's Steam/QAM and close
the local menu so the host's shows through.

iOS 27's GCControllerHomeButtonSettingsManager deep-link is a TODO (the
class needs the Xcode 27 SDK to compile). Docs: input, client-settings,
steam-deck. Design: punktfunk-planning design/system-buttons-routing.md.

Gates: docker clippy --all-targets --locked -D warnings + tests
(pf-client-core 88 incl. 6 new gesture tests, pf-console-ui 47),
cargo fmt --all --check, swift build (macOS), gradle kit+app compile,
decky tsc --noEmit + py_compile. clients/windows not compiled (no box).

docs-site/content/docs/client-settings.md

@@ -193,6 +193,21 @@ which forwards *every* connected controller, each as its own player, on Linux, W
 console home. Pinning one restricts the session to that controller alone — single-player. The Android
 app has no such picker.
 
+**Steam / guide button** (*Guide button* on Apple and Android) — *default: Automatic*, on every
+client. Where the guide (Xbox/PS/Steam) and quick-access presses go while streaming: **Send to
+host** forwards them raw, **This device** keeps them local. Automatic forwards everywhere except
+Gaming Mode, where SteamOS opens its own menus for those buttons no matter what — forwarding raw
+there opens *both* menus at once, the local one covering the stream. The full story, including how
+to reach the host's menus when the raw press stays local, is on the
+[Input page](/docs/input#the-guide-button-xbox--ps--steam-and-quick-access).
+
+**Hold Select for guide** — *default: Automatic*, on every client. The gesture that presses the
+host's guide button from any controller: hold Select (Back/View) on its own for about a third of a
+second, and keep holding for the host's long-press (a Gaming-Mode host's Quick Access Menu, on a
+regular pad). Automatic arms it only where the raw guide press can't reach the host cleanly —
+Gaming Mode, iPhone/iPad, Apple TV — because the gesture has a cost: a Select *tap* arrives a beat
+late, and a game that expects a *held* Select would trigger it. Set **On** or **Off** to overrule.
+
 **Capture system shortcuts** — *default: on.* Offered by the Linux and Windows apps, the console home
 and Decky; Windows spells the row out as *Capture system shortcuts (Alt+Tab, Win, …)*. On a Deck it
 matters only for a keyboard you attached yourself, for the reason the paragraph below gives: Gaming

docs-site/content/docs/input.md

@@ -98,6 +98,39 @@ there the client stops opening the controller at all, which is the point of the
 **Ctrl+Alt+Shift+D** or the client's own UI to leave instead. The Apple and Android apps keep
 watching for the chord either way.
 
+### The guide button (Xbox / PS / Steam) and Quick Access
+
+A controller's **guide button** — the Xbox logo, the PS button, the Deck's **Steam** button — is
+meant to open menus **on the host**: the Steam overlay, or a Gaming-Mode host's Steam menu. Some
+devices want that button for themselves, so every client also carries a gesture that works
+everywhere:
+
+**Hold Select (Back / View) on its own for about a third of a second.** The host sees its guide
+button go down, and it stays down for as long as you hold — so keeping it held reads as a long
+press on the host, which is how SteamOS opens the **Quick Access Menu** for a regular pad. A quick
+tap of Select still reaches the game, delivered when you let go (a beat late). Select pressed as
+part of a combo — including the leave chord above — passes through untouched.
+
+What the raw button does, per client:
+
+- **Linux & Windows desktop, macOS, Android** — the guide press is forwarded to the host. If
+  Steam Big Picture or the Xbox Game Bar is also watching for it *on the device in your hands*,
+  both may react — that's a local setting on that device, not something the stream can suppress.
+- **Steam Deck / Gaming Mode** — the **Steam** and **`…`** buttons stay with the Deck by default:
+  SteamOS always opens its own menus for them, so forwarding the raw press as well opened BOTH
+  menus at once, the Deck's on top of the stream. Reach the host's menus with **hold-Select**, or
+  with the Punktfunk panel's **Host menus** buttons ([Steam Deck page](/docs/steam-deck)). The
+  old behavior is one setting away: **Steam / guide button → Send to host**.
+- **iPhone / iPad** — iOS reserves the Home press for its own Game Overlay, so hold-Select is the
+  reliable route to the host's overlay. On iOS 27 or later you can also hand the button to the
+  app yourself, in the system's per-controller Home-button setting.
+- **Apple TV** — tvOS never delivers the Home press to apps; hold-Select is the only route.
+
+Both halves are [settings](/docs/client-settings#input), per profile like everything else:
+**Steam / guide button** (Automatic / Send to host / This device) and **Hold Select for guide**
+(Automatic / On / Off). Automatic picks the behavior above for each platform — the gesture stays
+off where the raw button already works, so games that use a *held* Select keep it.
+
 ## Mouse modes
 
 There are two, and they are a per-client setting called **Mouse input**:

docs-site/content/docs/steam-deck.md

@@ -111,6 +111,15 @@ for about a second and a half, or close the "game" from the Steam overlay. Eithe
 and drops you straight back to Gaming Mode. A quick press of the same four only releases captured
 input, so it is safe to hit by accident.
 
+**The Steam and `…` buttons stay with the Deck while streaming.** SteamOS opens its own menus for
+them no matter what, so forwarding the raw press as well opened *both* menus at once — the Deck's
+covering the stream. To reach the **host's** menus instead: **hold Select** for the host's Steam
+menu ([how it works](/docs/input#the-guide-button-xbox--ps--steam-and-quick-access)), or open the
+Punktfunk panel — while a stream runs it grows a **Host menus** section whose two buttons,
+**Steam menu on host** and **Quick access on host**, press the button on the host and close the
+Deck's own menu so the host's shows through. Want the raw forwarding back? Settings →
+**Steam / guide button** → *Send to host*.
+
 ## Updating
 
 The plugin **checks for updates itself** — no Decky store needed. It covers **both** the plugin *and*