Add ability to Suspend on LidSwitch from Lockscreen

### Feature Description

**Current Behaviour**
When in the DMS lockscreen, closing the laptop lid does not suspend the system, even though `HandleLidSwitch=suspend` in `/etc/systemd/logind.conf`

Also note that closing the lid from the desktop (not the lockscreen) works as expected.

**Expected Behaviour**
It would be great if the system would immediately suspend/shut off screen/etc... when the lid is closed.

### Use Case

Especially useful for OLED display users to avoid burn-in/laptop users to preserve battery life.

### Compositor(s)

- [x] All compositors
- [ ] Niri
- [ ] Hyprland
- [ ] MangoWC (dwl)
- [ ] Sway
- [ ] Other (specify below)

### Proposed Solution

An option in DMS settings to specify behaviour.

### Alternatives/Existing Solutions

You can manually suspend the system before closing the lid. Or close the lid from the desktop, and not from the lock screen.

No files, tests, or entry points are identified in the issue. Start by tracing how the DMS lockscreen handles lid-close events and how desktop lid handling delegates to systemd logind, then determine how the behavior can work across all listed compositors. Done means closing the lid from the lockscreen suspends or turns off the screen according to the chosen setting.

Written by the indexing model from the issue text.