Issue seems to be resolved, me and fellow Redditors are able to authenticate again.
Since this is obviously a server-sided problem (auth servers responding with a 503 error code), we just have to wait for a fix from Mojang/Microsoft. Save your efforts - any troubleshooting on the client-side (your side) won’t really help.
Issue seems to be resolved, me and fellow Redditors are able to authenticate again.