Give focus modes conditions rather than alarms, and let Gaming hand over

A mode is on because something is true right now: a game is running, a window is
fullscreen on a given display, a workspace is focused, the clock is inside a
window. That is asked again rather than fired once, and it is the whole reason
schedules could be included here without the usual failure modes. A machine
asleep at 23:30, rebooted at 02:00, or opened at 08:00 into a window that has
already passed all reach the right answer by being asked again; an alarm gets
all three wrong.

The midnight-crossing rule is the part worth being careful about: a window
belongs to the day it STARTS on, so a Friday-only 23:30-07:00 covers Saturday
morning and must not cover Saturday night. That arithmetic was tested as pure
logic before anything was built on it, including every malformed input failing
closed -- silencing someone because a time string was wrong is the worst way
this could fail.

This does not take over the manual timed session. FocusSession already owns
that, with its capsule, shortcut, Quick Settings entry and contracts, so modes
defer entirely while one runs. Two writers of Do Not Disturb would each restore
whatever the other happened to leave behind.

Gaming hands over rather than being duplicated. The hook was silencing
notifications itself, which would have made exactly those two owners -- and
Gaming.active only polls while its settings page is open, so a mode could not
have seen a game reliably in any case. The hook reports the game over IPC now
and the mode decides what that means, the Gaming page points at it, and
gamingSilenceNotifications is retired from the schema, since a setting nothing
reads is the dead row this work keeps removing.

Sleep ships disabled. A desktop that starts silencing someone on first boot has
overstepped, whatever the default hour.

Three contracts moved with it. gaming-contract asserted the hook uses setDnd,
which was right before and wrong now; the shell-side assertions that setDnd and
dndState exist stay, because a toggle would flip an already-silent machine back
on. The new contract is proven to fail by breaking the midnight rule and by
letting modes run alongside a manual session.

Claude-Session: https://claude.ai/code/session_01BRvzt4H8XXLPVH5MyYdk9L

config/local/share/vicinae/scripts/settings-desktop.sh

@@ -5,6 +5,6 @@
 # @vicinae.mode silent
 # @vicinae.icon ../../icons/hicolor/scalable/apps/panama-settings.svg
 # @vicinae.description Open Desktop & Dock in Settings.
-# @vicinae.keywords ["settings", "automatically hide the dock", "icon size", "reveal delay", "hide delay", "focus session length", "resize by dragging the border", "border grab area", "show the resize cursor", "snap distance between windows", "snap distance to screen edges", "snapping respects gaps", "master area size"]
+# @vicinae.keywords ["settings", "automatically hide the dock", "icon size", "reveal delay", "hide delay", "focus modes", "focus session length", "resize by dragging the border", "border grab area", "show the resize cursor", "snap distance between windows", "snap distance to screen edges", "snapping respects gaps"]
 
 exec "$HOME/.config/quickshell/scripts/panama-action" settings-page desktop

config/local/share/vicinae/scripts/settings-gaming.sh

@@ -5,6 +5,6 @@
 # @vicinae.mode silent
 # @vicinae.icon ../../icons/hicolor/scalable/apps/panama-settings.svg
 # @vicinae.description Open Gaming in Settings.
-# @vicinae.keywords ["settings", "use the performance power profile", "silence notifications", "say when game mode engages", "game mode", "performance overlay", "proton", "graphics card"]
+# @vicinae.keywords ["settings", "use the performance power profile", "say when game mode engages", "game mode", "performance overlay", "proton", "graphics card"]
 
 exec "$HOME/.config/quickshell/scripts/panama-action" settings-page gaming