You mean you don't get the following window if you run the launcher while Steam is not running?
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Because this is what I can see unless Steam is already running. In which case it insists that I log in with Steam, every single time:
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The old launcher did not have this issue. It was just working 100% of the time, regardless of Steam.
No such screens for me.
The important part is to log into the launcher with the email and password of your Frontier account, and NOT with the credentials of your Steam linked account.
This happened exactly the same with the old launcher, btw...