Fix online status not persisting correctly

[peppy]

Regressed at some point. Can't find why but oh well.

I don't see much reason not to link the bindable directly with config. It seems to work as you'd expect. Tested with logout (resets to "Online") and connection failure (persists). Not going to overthink this until we have full support for it.

Closes #29173.

[bdach]

fef8afb833b7ddfd42b97260faff7593da514868 is the first bad commit
commit fef8afb833b7ddfd42b97260faff7593da514868
Author: Dean Herbert <pe@ppy.sh>
Date:   Fri Mar 29 12:03:05 2024 +0800

    Fix double binding causing game crash after API enters failing state
    
    See https://sentry.ppy.sh/organizations/ppy/issues/33406/?alert_rule_id=4&alert_timestamp=1711655107332&alert_type=email&environment=production&project=2&referrer=alert_email

 osu.Game/Overlays/Login/LoginPanel.cs | 17 +++++++++++++----
 1 file changed, 13 insertions(+), 4 deletions(-)

[bdach]

i guess this doesn't seem broken