Remove the swayidle compatibility backend

[Staphylococcus]

Parent: #21

Phase: v2.0.0 cleanup after native Wayland promotion and the delegated-backend compatibility window.

Blocked by: #86

Goal

Complete the native Wayland migration by removing the delegated swayidle runtime backend and its external dependency, configuration surface, installer wiring, tests, and documentation.

Scope

• Remove ScreenBackend::Swayidle and swayidle as a current screen_backend / screen.backend choice.
• Remove delegated process execution and shell command construction from the session runner.
• Remove swayidle command probing, capability models, and backend detection branches.
• Remove the sources/desktop/swayidle.rs adapter.
• Remove mock swayidle executables, fixtures, feature scenarios, and support code after native coverage protects the equivalent product behavior.
• Remove installer prerequisite checks and package-install guidance for swayidle.
• Remove obsolete architecture, backend-model, runtime-event, development, testing, and user documentation.
• Update release-bundle smoke coverage to prove the package has no delegated idle-backend dependency.
• Give stale explicit screen_backend=swayidle configurations a clear migration or validation error.

Acceptance criteria

• Non-GNOME Wayland idle/activity behavior is fully handled by the native provider.
• Runtime and installer paths do not execute, probe, install, or recommend swayidle.
• Fresh and existing supported configurations resolve without a delegated backend.
• A stale explicit swayidle value produces an actionable migration message.
• Native timeout, activity, auxiliary gamepad, restart recovery, provider recovery, and backend-selection coverage replaces the removed mocks.
• The musl release bundle and smoke tests pass without a swayidle runtime dependency.
• Documentation no longer describes delegated swayidle as supported.

Out of scope

• New native Wayland protocol work beyond compatibility fixes needed for removal.
• Changes to GNOME monitoring.
• Changes to gamepad activity semantics.
• Changes to logind lifecycle, screen policy, ownership markers, or restore policy.
• Broad installer-layout work tracked by Support immutable distro install layouts #24.