Perhaps consider moving the site to Firebase and put Firebase Authentication in front of it (believe the author piece is free based on https://stackoverflow.com/questions/44161195/which-pricing-t...) ? Firebase services also have a general free tier (although may not be suitable to your use case if course), and many paid pricing levels.

For $15 p/mth, you have a couple of options with Aerobatic [0].

Option 1 is using the Auth0 plugin [1, 2] Option 2 is using the Password Protect plugin [3]

Disclaimer: I work for Aerobatic.

[0] https://www.aerobatic.com/

[1] https://www.aerobatic.com/blog/announcing-auth0-plugin/

[2] https://www.aerobatic.com/docs/plugins/auth0/

[3] https://www.aerobatic.com/docs/plugins/password-protect/

Looks like the only way to do this is to proxy all request to the static server through an authentication server, and you could write the authentication server in any language.

[authentication server] -> [static server]

Unfortunately, this kind of defeats the purpose of having a static server.

I would use Wordpress