This PR addresses some post-merge issues caught by @davidegiacometti,
including:

1. Separator in the context menu shown when not running from inside
PowerToys.
2. "Keep display on" setting not persisting across switches between
modes.
3. Awake not launching in standalone mode.

Additionally:

1. Exits are now properly handled in **timed** and **expirable**
keep-awake modes when running standalone. This ensures that Awake exists
after completion and doesn't switch to an in-actionable passive mode.
2. Tray tooltips now cover how much time is left on the timer.
3. Fixes #29354
4. Avoids a nasty memory leak because of re-instantiating of `Icon`
objects for every tray update.
5. Adds DPI awareness to the context menu (#16123)