First, the dockerfile is the following, direcly generated by phoenix. I commented assets related stuff (compile and deploy)

# Find eligible builder and runner images on Docker Hub. We use Ubuntu/Debian instead of
# Alpine to avoid DNS resolution issues in production.
#
# https://hub.docker.com/r/hexpm/elixir/tags?page=1&name=ubuntu
# https://hub.docker.com/_/ubuntu?tab=tags
#
#
# This file is based on these images:
#
#   - https://hub.docker.com/r/hexpm/elixir/tags - for the build image
#   - https://hub.docker.com/_/debian?tab=tags&page=1&name=bullseye-20210902-slim - for the release image
#   - https://pkgs.org/ - resource for finding needed packages
#   - Ex: hexpm/elixir:1.13.3-erlang-24.2.1-debian-bullseye-20210902-slim
#
ARG BUILDER_IMAGE="hexpm/elixir:1.13.3-erlang-24.2.1-debian-bullseye-20210902-slim"
ARG RUNNER_IMAGE="debian:bullseye-20210902-slim"

FROM ${BUILDER_IMAGE} as builder

# install build dependencies
RUN apt-get update -y && apt-get install -y build-essential git \
    && apt-get clean && rm -f /var/lib/apt/lists/*_*

# prepare build dir
WORKDIR /app

# install hex + rebar
RUN mix local.hex --force && \
    mix local.rebar --force

# set build ENV
ENV MIX_ENV="prod"

# install mix dependencies
COPY mix.exs mix.lock ./
RUN mix deps.get --only $MIX_ENV
RUN mkdir config

# copy compile-time config files before we compile dependencies
# to ensure any relevant config change will trigger the dependencies
# to be re-compiled.
COPY config/config.exs config/${MIX_ENV}.exs config/
RUN mix deps.compile

COPY priv priv

# note: if your project uses a tool like https://purgecss.com/,
# which customizes asset compilation based on what it finds in
# your Elixir templates, you will need to move the asset compilation
# step down so that `lib` is available.
# COPY assets assets # My app has no-assets

# compile assets
# RUN mix assets.deploy

# Compile the release
COPY lib lib

RUN mix compile

# Changes to config/runtime.exs don't require recompiling the code
COPY config/runtime.exs config/

COPY rel rel
RUN mix release

# start a new build stage so that the final image will only contain
# the compiled release and other runtime necessities
FROM ${RUNNER_IMAGE}

RUN apt-get update -y && apt-get install -y libstdc++6 openssl libncurses5 locales \
  && apt-get clean && rm -f /var/lib/apt/lists/*_*

# Set the locale
RUN sed -i '/en_US.UTF-8/s/^# //g' /etc/locale.gen && locale-gen

ENV LANG en_US.UTF-8
ENV LANGUAGE en_US:en
ENV LC_ALL en_US.UTF-8

WORKDIR "/app"
RUN chown nobody /app

# Only copy the final release from the build stage
COPY --from=builder --chown=nobody:root /app/_build/prod/rel/worklist ./

USER nobody

CMD ["/app/bin/server"]

Second, I did try with my ip in DATABASE_URL, but nothing changed.

My end goal would be to use docker compose with my app and postgres as services. But trying to use compose when I can’t make a container run correctly seem a bit out of order.

You can connect to services running on the host machine from a docker container directly using the special hostname:

host.docker.internal

See: https://docs.docker.com/desktop/windows/networking/#use-cases-and-workarounds

(the link is about Windows, but it also works on Mac)

For linux you will need to add following line to your service needs to access localhost-

extra_hosts:
      - "host.docker.internal:host-gateway"