After attempting the initial connection to Google Photos API, your browser will be redirected to an address like:
http://localhost:51894/google-photos?state=state_parameter_passthrough_value&code=d35fEac9&scope=https://www.googleapis.com/auth/photoslibrary.readonly
Instead of redirecting you back to Obsidian, you might see an error message like this:
Unable to connect
localhost refused to connect
ERR_CONNECTION_REFUSED
In this case, there is a workaround:
Change the URL in your browser to replace http://localhost:51894/ with obsidian://, so that the final result looks similar to:
obsidian://google-photos?state=state_parameter_passthrough_value&code=d35fEac9&scope=https://www.googleapis.com/auth/photoslibrary.readonly
Press Enter to go to that URL, and Obsidian should launch and complete the authentication process.