if the actual end app is not on the same based domain (not a sub domain) of the SSO domain, then it would require supertokens to be an oauth provider. You can use us to build the implicit oauth flow (which i know is deprecated), right now, but if you want the authorisation code grant flow, then you will have to wait for us to release the oauth feature.
If it's across sub domains, you can share session cookies across sub domains and it would work.