Following ChatGPT's advice, I implemented the PKCE flow for authentication while letting the server get the code at the last stage, and ask for the token itself to register the user in my DB. All while the Nuxt proxy is in place, and forwards API requests.

This worked out, and my authentication now works for Brave and Safari. However, the proxy led me to other issues. Due to the game nature of my app which requires websocket connections and fast interactions, that is hindered by the proxy. So I'm going to seek a solution to bring my API and frontend to the same domain.