Temporary solution
This does not completely solve the problem for production purposes, but at least in order to get the localhost working, by adding these lines into docker-compose.yml it solved my issue for now (source):
services:
my-service:
network_mode: host
I am using apache nifi to use Java REST endpoints with the same ubuntu and docker versions, so in my case, it looks like this:
services:
nifi:
network_mode: host
After changing docker-compose.yml, I recommend stopping docker container, removing containers(docker-compose rm - do not use if you need some containers, otherwise use docker container rm container_id) and build with docker-compose up --build again.
In this case, I needed to use another localhost IP for my service to access with a browser (nifi started on other ip - 127.0.1.1 but works fine as well).
Searching for the problem / deeper into ubuntu-docker networking
Firstly, I will write down some useful commands that may be useful to find out a solution for the docker-ubuntu networking issue:
ip a - show all routing, network devices, interfaces and tunnels (mainly I can observe state DOWN with docker0)
ifconfig - list all interfaces
brctl show - ethernet bridge administration (docker0 has no attached interface / veth pair)
docker network ls - manages docker networks - names, drivers, scope...
docker network inspect bridge - I can see for docker0 bridge has no attached docker containers - empty and not used bridge
(useful link for ubuntu-docker networking explanation)

I guess that problem lays within veth pair (see link above), because when docker-compose occurs, there is a new bridge created (not docker0) that is connected to veth pair in my case, and docker0 is not used. My guess is that if docker0 is used, then host.docker.internal:host-gateway would work. Somehow in ubuntu networking, there is docker0 not used as the default bridge and this maybe should be changed.
I don't have much time left actually, well, I suppose someone can use this information and resolve the core of the problem later on.