Can't access configured service locally

No, local access to published ports or directly to aqua container ports should just work.
I assume you are using the jitsi container from your howto, I’d like to use it to setup jitsi for testing asap.
I tested with a simple nginx container by running

docker run --name mynginx1 -p 8080:80 -d nginx

Then I put it to aqua network via portainer like you described in the howto and the test connection worked.

[root@testserver ~]# curl localhost:8080
<!DOCTYPE html>
<html>
<head>
<title>Welcome to nginx!</title>
...

curl 172.28.0.2 is working too (direct access to nginx container)

Did you put the container to the aqua network? Because br-... seems to be another network.