How does this part work? It's unclear to me how a web/mobile app should be posting to a forum. It's invoking an API that exists on a server (client-side code is not secure). Perhaps I'm picturing your model wrong..
Maybe a better example is say you have a Dropbox camera app. You originally created your Dropbox account using "Sign up with Google". You launch the app, and say "show me my photos". Dropbox is the client, Google is the OpenID provider and tells Dropbox who you are, and the thing Dropbox is doing on behalf of "the user who uploaded the photos" is "sending them over the internet to the user asking for them".
The important thing here is Google doesn't have anything to do with photos, all it does is know who you are. The party that can actually do things is Dropbox, who is storing your photos.
Your example includes two separate OAuth/OIDC flows. Dropbox as the client to Google, and the camera app as a client to Dropbox.