Docker Compose: How do you build an image while running another container?

I'm trying to build a Nuxt 3 application using docker compose. However, I'm having trouble with docker compose and dockerfile configuration.
Context

To give background on the project that I'm working on, here are the stack that I'm using:

• Nuxt 3 for SSG

• Strapi for CMS

• Nginx for serving static contents generated from Nuxt 3

So, in Nuxt 3 I can run npx nuxi generate to pre-render/generate static contents for the website. After generating the static HTML files, nginx will serve the static contents. Strapi will serve as headless CMS, providing contents for the website.
Problem

The problem is that, when pre-rendering a static contents in Nuxt 3, it requires Strapi backend to run so that it can fetch the contents from Strapi CMS and generate the html files.

So in terms of command line, I need to make sure that Strapi server is running (strapi start) and only then generate the static files (npx nuxi generate) or else there would be an error during build process because Nuxt application cannot fetch resource from the strapi server.

When using docker, I need to make sure that Strapi server container is running while building the Nuxt/node.js image. However, I don't know how I'm supposed to run a container (strapi server) while building an image (Nuxt SSG contents).
Files

Dockerfile.client

# Nuxt Image
FROM node:16-alpine as build
WORKDIR /app
COPY ./client .
RUN npm install
RUN npm run generate

# Nginx Image
FROM nginx:1.15 as publish
COPY --from=build /app/.output/public/ /usr/share/nginx/html
COPY ./nginx/nginx.conf /etc/nginx/conf.d/default.conf
EXPOSE 80
ENTRYPOINT ["nginx", "-g", "daemon off;"]

Dockerfile.server

```
# Strapi Image
FROM node:16-alpine
# Installing libvips-dev for sharp Compatability
RUN apk update && apk add build-base gcc autoconf automake zlib-dev libpng-dev nasm bash vips-dev
ARG NODE_ENV=production
ENV NODE_ENV=${NODE_ENV}
WORKDIR /opt/
COPY ./server/package.json ./server/yarn.lock ./
ENV PATH /opt/node_modules/.bin:

You could try using the --profile option during the build.

version: "3"
services:
  strapi:
    profiles: ["strapi"]
    build:
      context: ./
      dockerfile: strapi/Dockerfile
    container_name: "strapi"
    restart: always
    ports:
      - "3000:3000"

  nuxt:
    build:
      profiles: ["nuxt"]
      context: ./
      dockerfile: nuxt/Dockerfile
    image: nuxt:latest
    container_name: "nuxt"
    restart: always
    ports:
      - "3000:3000"

Then pass the profile switch during the build:

docker compose --profile nuxt build

Please refer to the official documentation for more information:

https://docs.docker.com/compose/profiles/

StackExchange DevOps Q#16822, answer score: 1