Access ports with specific address

I’ve set up Pi-hole to manage my network, and it is installed on a Raspberry pi 4 that already handles some stuff, for instance, an R-shiny server on port 3838 and a homeassistant installation on port 8123.

I want these services to be accessible through user-friendly addresses.

I added a local DNS entry so that http://raspi.local redirects to my raspberry pi, but I obviously have to add the port to the address for this to work.

I have very little knowledge of networks and maybe a little over my head here. I read everywhere that DNS has nothing to do with ports, neither /etc/host.

How could I access my services through pretty addresses such as http://raspi.local/shiny (port 3838) and http://raspi.local/homeassistant (port 8123)?

EDIT – what I’ve tried so far:

• in Pi-hole, setting an IP with the port after a # or a : " throws Error while adding this custom DNS entry
• looking up mod_proxy in Lighttpd configuration (/etc/lighttpd/external.conf) but with no sucess so far