You have set up cross save backwards. You picked your Steam account with no characters to be the cross save account. That is why you're presented with a create a new character prompt on Stadia and Steam.
If your intention was to make the Stadia account the cross save account then go to this page, https://www.bungie.net/en/Help/Troubleshoot?oid=48099 and scroll to the bottom where there is a contact form link. Click it and fill in the information requesting Bungie to switch your cross save account from Steam to Stadia.
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EggoEdalyn Clawthorne - old
How did it end up being the other way around? I never ever played on Steam before, only Stadia, I wanted my Warlock to cross save TO steam, but it somehow did the opposite, I'll fill in the request, thank you!