HAProxy is primarily used as a load balancer. (HA = high availability) The feature sets of it and Nginx have lots of overlap (including reverse proxy), but HAProxy does not serve pages (aside from error pages), so you will need Nginx or another real webserver somewhere.

I use HAProxy to terminate TLS and HTTP/3, route to other webservers based on subdomain, and reverse proxy/cache. I'm 100% sure Nginx can do all that, though.