Looks like some EU players are still reporting login issues. Unfortunately we must wait for Valve to investigate further.
Praise our lord Gaben for a swift recovery

and it works now, atleast for me
Yeah, weāre seeing intermittent reports of some people being able to log in through Steam while otherās still canāt. We canāt see anything on our end beyond authentication attempts, and now weāre only seeing successful auths. (Previously we were seeing a āUser is offlineā error)
UK Player here - still no joy at the moment.
Yep, German player here, still offline, too. Lets hope Valve finds the problem fast.
I was still getting the error but cleared the download cache in the Steam client and this has now resolved the issue for me.
Steam > Settings > Downloads > Clear Downloads Cache
I have made 2 attempts within the last half hour. Steam client in the U.S.
Iāll try again later. 
Iām very curious to see if others report success from this. Thanks for the suggestion!
2 out of 2 successes so far for this fix. Excellent sleuthing, Tropes!
Iāve tried this. It didnāt seem to resolve my issue.
Iām a European user.
Something I saw from Discord:
Seems to have worked for a couple people, too.
That seemed to do it. Thank you!
Playing from Singapore and no luck logging in today as well, so it seems like the Steam login issues are happening in Asia as well, not just Europe.
Playing from Russia. Canāt login all day. Neither of the aforementioned fixes forked for me.
UPD: Disabling the antivirus seems to have solved the issue one time, but when I tried doing it again, it didnāt help.
I tried logging in and was unable to do so at first.
Following the above suggestions, I cleared the download cache, but could not log in afterwards.
Then I tried logging in waiting 5 seconds and canceling out.
After 6 times I was able to log in.
I hope this helps other people.
Did not resolve mine either, playing from Asia (Singapore)
I did the cache clearing thing & could log in. Then I logged out of the game & couldnāt log in again.
I tried the cache clearing thing again, and now that didnāt work either.
So, I then tried method 2, and after about 15 attempts, I could login again.
This is very annoying.
(Playing from Australia.)
Same as Fernando now - except I needed 8 attempts. (UK - Euro based)
Cancel login and try again worked for me on second try. Yay!