maptiler-server & nginx proxy to a URL with sub-folder

[wxrl]

OS: Debian 12 with nginx 1.22.1 Maptiler: maptiler-server 4.4.0 directly installed with .deb package

After installation I can proxy http://127.0.0.1:3650 to http:// or https://xxx.mydomain.com but kept failing to proxy it to https://xxx.mydomain.com/map

There are some parameters I found here baseurl and public_url, neither of them worked no matter I used them in the maptiler-server execution command or in the config.json. Could anyone suggest? Thanks.