feat(decky): self-update without the store + Gaming-Mode launch polish, and ship the Steam Deck docs

Plugin self-update (no Decky store): CI publishes a per-channel manifest.json
({version, immutable per-version artifact, sha256}) beside the zip and bakes
update.json {channel, manifest} into the plugin. main.py `check_update` reads the
installed version from package.json (the value Decky reports — not plugin.json),
fetches the channel manifest, and the frontend shows an "Update to vX" button that
drives Decky Loader's own install RPC (root downloads + SHA-256-verifies + hot-reloads).
CI now stamps a plain-numeric semver (0.3.<run> canary / X.Y.Z stable) into
package.json — a -ciN suffix would mis-order under compare-versions.

Linux client: `--fullscreen` (plus SteamDeck/gamescope env fallback) enters GTK
fullscreen on stream start so Gaming-Mode chrome is hidden; native-mode resolution
falls back to the display's first monitor when the window isn't mapped yet (was
dropping to the 1080p floor — wrong on the Deck's 1280×800); add a confirmed
"Remove saved host" action (KnownHosts::remove_by_fp).

Docs: new docs/steam-deck.md (Decky install/pair/stream/self-update/troubleshooting),
wired into meta.json nav, and cross-linked from clients/install-client/channels. This
is the page docs.punktfunk.unom.io/docs/steam-deck — the website's download link
pointed at it before it existed; committing it makes that link resolve.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

clients/decky/src/backend.ts

@@ -5,8 +5,9 @@ export interface Host {
   name: string;
   host: string;
   port: number;
-  pair: string; // "required" | "optional"
+  pair: string; // "required" | "optional" — the HOST's policy
   fp: string;
+  paired: boolean; // whether THIS device has already PIN-paired this host (by fingerprint)
 }
 
 export interface PairResult {
@@ -32,6 +33,16 @@ export interface StreamSettings {
   mic_enabled: boolean;
 }
 
+export interface UpdateInfo {
+  current: string; // installed version (package.json)
+  latest: string; // newest version in our registry for this channel
+  artifact: string; // immutable zip URL Decky should install
+  hash: string; // sha256 of that zip (Decky verifies it)
+  channel: string; // "latest" (stable) | "canary"
+  update_available: boolean;
+  error?: string; // "update-channel-unknown" (dev build) | "fetch-failed"
+}
+
 export const discover = callable<[], Host[]>("discover");
 export const pair = callable<
   [host: string, port: number, pin: string, name: string],
@@ -43,3 +54,4 @@ export const setSettings = callable<[settings: StreamSettings], { ok: boolean }>
   "set_settings",
 );
 export const killStream = callable<[], { ok: boolean }>("kill_stream");
+export const checkUpdate = callable<[force: boolean], UpdateInfo>("check_update");