status/keyboard: Fix execution order when activating source

status/keyboard: Fix execution order when activating source

When commit ce89b15bb123d made the code async, it did not only
delay releasing the keyboard until after the engine has been
updated, but also the following code that updates the current
input source.

One result is that the current source is now initialized later,
which breaks any code that relies on the source being set.

This affects the login screen in particular (which uses different
`InputSourceSettings` than the regular session): It fails to come
up entirely if the OSK is enabled.

To fix the issue, use a .then() callback to release the keyboard,
instead of blocking all following code with await.

Fixes: ce89b15bb1 ("ibusManager: Use async await instead of callbacks")
Closes: https://gitlab.gnome.org/GNOME/gnome-shell/-/issues/7912
Part-of: <https://gitlab.gnome.org/GNOME/gnome-shell/-/merge_requests/3476>