logind: fix closing of button input devices

This is a fix of #17751. Specifically:

1. Sort #include headers again

2. Remove tabs, as per coding style

3. Don't install fds in half-initialized objects

4. Use asynchronous_close() everywhere

That all said:

Quit frankly, I am not convinced we should do all this at all. If
close()ing of these input devices is really that slow, then this should
probably be fixed in the kernel, not worked around in userspace like
this.