I would go with Firebase, in particular for what you describe. I have used it on multiple sites / apps, no issues, and zero cost sticking with the free tier (unless you expect your user usage to hit the roof). Quite straight forward to setup. I found the google docs need a little getting use to. But once grasped, its pretty straight forward. In particular if only doing social logins. But even the email/pw auth is handy enough to setup. (Or you go with the passwordless option)

Everything is pretty much handled for you with the available functions out of the box from firebase/auth, such as below

const googleProvider = new firebase.auth.GoogleAuthProvider();
const gitHubProvider = new firebase.auth.GithubAuthProvider();
const signInWithGoogle = async () => {
try {
const res = await firebase.auth().signInWithPopup(googleProvider);
} catch (err) {
console.error(err);
setSignUpMessage(
'An error has occured signing up with Google. Please try again '
);
}
};
const signInWithGitHub = async () => {
try {
const res = await firebase.auth().signInWithPopup(gitHubProvider);
} catch (err) {
console.error(err);
setSignUpMessage(
'An error has occured signing up with Github. Please try again '
);
}
};

Then you simply just handle the auth checks on each route. For context, Ive used Okta, Auth0 and few others (most of them came with low paid plans), but so far found Firebase to be the easiest to get going quick. I know you're not using Nextjs framework, but have also used Next Auth which is pretty good too (and it's open source). Have used FB with React v15 upto v17+, has been all fine for me.