If you want to do this yourself, caddy http server [0] works really well and is incredibly easy to use / setup. They even have an example on their home page that shows this for /api and /blog
It's trickier than it seems, though, because you need to get the right combination of Host/X-Forwarded-Host right for a given hosting service. And you frequently need to rewrite HTML to fix links. Not rocket surgery, but usually I'd rather put my hours into dev and not tweaking a proxy.
This is exactly what I use to run a bunch of different personal services in subfolders on the same hostname. Sadly, though some things don't support running in subfolders.
Pretty specific use-case, but if you use Rancher for Docker orchestration, the built-in load-balancer service that you can deploy makes this pretty easy.
[0] https://caddyserver.com/