Solution for this from experimenting and Webflow support:
Initially I tried creating a new account in Stripe during the auth process on Webflow Ecommerce, which allowed me to connect the two without the API error.
Then support replied to my query saying that you will most likely be getting the API error if you already have a Webflow Eccomerce site connected to the same Stripe account, which was the case for me.
So by creating a new Stripe account, I was able to successfully connect the two.
In short, one Webflow site + one Stripe account, else you will get the API error.
Either disconnect the previous Webflow site, or create a new Stripe account.
All the best.