Keep Awake even when lid is closed

### Feature Description

Add an option to `Keep Awake` to also inhibit sleep when closing the lid. And ideally the screen should still turn off as it will save on battery and doesn't need to be on if the lid is closed.

### Use Case

When I want sleep inhibited, it's usually because I want to close the lid of my laptop and take it to go, while it is still running a long-running command.

### Compositor(s)

All compositors

### If Other, please specify

_No response_

### Proposed Solution

_No response_

### Alternatives/Existing Solutions

Right now, I'm still relying on my systemd-inhibit command (`systemd-inhibit --what=sleep --who="$USER" --why="why not" sleep infinity`) until this gets added.

Start by tracing the existing Keep Awake option and its systemd-inhibit integration. Check how lid-close sleep and screen power behavior are handled across the supported compositors; done means the option prevents sleep with the lid closed while still allowing the screen to turn off.

Written by the indexing model from the issue text.