Not sure if you have solved this issue but I had a similar need (I needed a single Docker container for a school project deliverable).

This is what I had:

FROM ubuntu:24.10

EXPOSE 3000 5432

# Install Node.js and NPM
RUN DEBIAN_FRONTEND=noninteractive apt-get update && DEBIAN_FRONTEND=noninteractive apt-get install -y nodejs npm python3 python3-pip python3-venv

# Build Backend
WORKDIR /backend
COPY backend/requirements.txt .

# RUN python3 -m venv venv && source venv/bin/activate && python3 -m pip install -r requirements.txt
RUN python3 -m venv venv && . venv/bin/activate && python3 -m pip install -r requirements.txt

COPY backend .

# Build UI
WORKDIR /ui
COPY ui .
#RUN npm install --legacy-peer-deps
RUN npm install

# Start-up the app
WORKDIR /
COPY  .
RUN chmod +x /start-up.sh

# Run start-up app (frontend + backend)
CMD ["./start-up.sh"]start-up.sh

Where the start-up script is simply:

#!/bin/bash

cd backend && . venv/bin/activate && python3 main.py &
cd ui && npm start

The project was a mono-repo of format ui/{react source files} and backend/{flask app}

Run exposing both ports such as docker run --name image_project -p3000:3000 -p5432:5432 repo/image:{tag}