HA-Proxy - trying to create different paths for my docker containers but only default_backend works

I have my haproxy container called 'proxy_container' running on port 80 on my localhost. With two other containers called 'client_container' which is just an html file, and 'server_container' which is a nodejs basic api I wrote. All connected to a single docker network called 'appnet'.

docker ps:

    CONTAINER ID   IMAGE          COMMAND                  CREATED              STATUS              PORTS                NAMES
f6fa17dbd444   ebdc86ff4850   "docker-entrypoint.s…"   About a minute ago   Up About a minute   80/tcp               server_container
32ebf717e9de   8657ad512e31   "/docker-entrypoint.…"   About a minute ago   Up About a minute   80/tcp               client_container
bc3f94b668cd   bd8334ffaaad   "docker-entrypoint.s…"   About a minute ago   Up About a minute   0.0.0.0:80->80/tcp   proxy_container

Here is my haproxy.cfg file:

global
    daemon
    maxconn 2000
    stats   socket /var/run/haproxy.sock mode 777

resolvers docker
    nameserver dns "${DNS_TCP_ADDR}:${DNS_TCP_PORT}" #127.0.0.11:53

defaults
    mode        http
    option      dontlognull
    option      forwardfor
    option      httpclose
    option      httplog
    retries     3
    timeout     check    5s
    timeout     client   5s
    timeout     connect  10s
    timeout     server   10s

frontend main
    bind *:80
    mode http
    option http-server-close
    option forceclose

    timeout client 60s
    timeout connect 10s
    timeout server 1m

    acl url_ui path_beg /home
    acl url_api path_beg /api
    use_backend ui if url_ui
    use_backend api if url_api

    #deafult_backend ui

backend api
    # mode http
    # server api server_container
    server api server_container.appnet:80 check resolvers docker resolve-prefer ipv4

backend ui
    # mode http
    # server client client_container
    server client client_container.appnet:80 check resolvers docker resolve-prefer ipv4

The default_backend ui line that I commented out worked fine when typing 0.0.0.0/ in my browser. I want to change my config so that 0.0.0.0/home directs me to backend 'ui', and 0.0.0.0/api directs me to backend 'api'.

Side question: for the api path how would my nodejs api paths work alongside these configurations I want?