TENTATIVE FIX:
To avoid this loop between the steam app and companion app, when you press sign in on the companion app and it brings up the page to select your platform. HOLD down on the steam option. It will pop out a preview screen of the steam website. Just click on the username part of the preview screen and it will allow you do do the sign in from the steam website while still on the companion app. After you sign into your steam account on the website, you can go open the steam app separately and confirm the sign in. Return to the companion app and approve the account link. This should allow the sign in to work. At least it did for me.
Hope it helps!
English
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Fantastic this has worked. Thanks so much