fix(vdisplay/gamescope): DM-flavor-aware session takeover — stop masking Nobara's plasmalogin to death

Field report (Nobara 43 HTPC): switching the host to Steam Game Mode
mid-stream permanently black-screened the box. Live-proven root cause on
a Nobara repro VM: our takeover masks the box's gamescope-session-plus
unit, plasmalogin's Relogin=true then fails its session Exec repeatedly
and trips systemd's start limit within ~1 s — the display manager dies,
and our restore verb (unmask + user start) cannot bring a seatless
gamescope back. Only 'reset-failed + restart' of the DM recovers.

The takeover is now display-manager-flavor-aware:
- SDDM (Bazzite/SteamOS) keeps the proven mask+SIGKILL path unchanged.
- plasmalogin/unknown DMs never mask: with privilege (root or an
  operator polkit rule scoped to the DM unit — documented) the host
  stops the DM for the stream and restores it with reset-failed +
  restart (PUNKTFUNK_RECOVER_SESSION_CMD as fallback), recorded in the
  persisted takeover state so a host crash still restores; without
  privilege the managed takeover degrades to ATTACH and mirrors the
  box's live Game Mode instead of destabilizing the seat. Both legs of
  the privileged cycle live-verified on the repro VM (headless managed
  session works with zero login sessions; render nodes are 0666).
  A loaded-but-inactive leftover instance never triggers the DM stop.

Companion fixes from the same triage:
- ensure_box_gamescope_mode gains the attach-only rebuild-probe guard
  both managed paths already had (stale post-capture-loss detection
  restarted the box's unit), and no longer re-modes a box that drives a
  physical display — attach mirrors on-glass; re-mode is the
  headless-box model.
- Capture-loss rebuilds targeting gamescope get a 100 s budget: the
  40 s budget expired inside the first 45 s Steam-cold-start launch
  attempt, a guaranteed single-shot failure.
- A PUNKTFUNK_COMPOSITOR pin now WARNs once per capture loss when the
  live session no longer matches it (the pin disables
  session-following — the reporter's original stream-death trigger).
- A managed session that took nothing over (client gamescope pin beside
  a live desktop) is stopped on disconnect instead of being orphaned
  forever.

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

docs-site/content/docs/troubleshooting.md

@@ -107,6 +107,21 @@ See [GNOME](/docs/gnome) for the GL/EGL userspace details.
   auto-detects the live compositor, and the pin points it at one backend even when a different
   session is live (it also disables Gaming ↔ Desktop following).
 
+## The screen stays black after switching to Game Mode (Nobara)
+
+On distros whose Game Mode is display-manager autologin under **plasmalogin** (Nobara), a managed
+takeover from a host **0.19.1 or older** could kill the display manager: it trips systemd's start
+limit and the box stays black until someone restarts it. Recover from a VT (Ctrl+Alt+F3) or SSH:
+
+```sh
+systemctl --user unmask --runtime 'gamescope-session-plus@*.service'
+sudo systemctl reset-failed plasmalogin && sudo systemctl restart plasmalogin
+```
+
+Current hosts detect the display-manager flavor and never mask the session unit there — see
+[gamescope → autologin display managers](/docs/gamescope) for the polkit rule that enables the full
+managed takeover on these boxes (without it the host mirrors Game Mode instead).
+
 ## Session fails right after editing host.env
 
 - Keys are **case-sensitive**: `punktfunk_gamescope_attach=1` sets nothing — use the exact