HAproxy is good at what it does but it’s only good at proxying and simple rules. For the most part, it’s used as a load balancer and router and doesn’t really process the requests itself.
To add something here: HAProxy’s ACLs are more powerful than anything nginx, Apache or even Envoy can do. Of course HAProxy is not a web server but “just” a reverse proxy that speaks HTTP (and TCP) but what you can do with its ACLs is often extremely impressive in its simplicity and elegance. A single-line ACL in HAProxy would require loading additional modules in nginx and writing a screenful of configuration directives. Though the average self-hoster will probably never need any of the power HAProxy offers.
In the past 20 years I have professionally used all four of these as web servers and/or reverse proxies and I am pretty confident that HAProxy beats all others when it comes to request processing. Though Envoy might be getting there.
And here I’ve been vacationing in Svenborgia, like a peasant!