[BUG] compose up --wait exits 1 on init containers successfully completing

Description

When using docker compose up --wait, where I have an init container that populates some data and then exits (0), docker compose will exit 1.

If any other container depends on the init container finishing, it will exit properly, as described/exampled in this PR: https://github.com/docker/compose/pull/9572. In my situation however, there is no container that runs a service that depends on the init container finishing.

Steps To Reproduce

docker-compose.yml example:

version: '3'

services:
  postgres:
    image: postgres:14-alpine
    environment:
      POSTGRES_DB: postgres
      POSTGRES_USER: postgres
      POSTGRES_PASSWORD: postgres
    healthcheck:
      test: ['CMD', 'pg_isready']

  postgres_setup:
    image: alpine
    depends_on:
      postgres:
        condition: service_healthy
    restart: "no"
    command: pwd

Run docker compose/print exit code:

$ docker compose up --wait
[+] Running 2/3
 ✔ Network test_default             Created                                                                                                                                                    0.1s
 ✔ Container test-postgres-1        Healthy                                                                                                                                                   31.9s
 ⠿ Container test-postgres_setup-1  Waiting                                                                                                                                                   31.9s
container test-postgres_setup-1 exited (0)

$ echo $?
1

Compose Version

Docker Compose version v2.17.3

Docker Environment

Client:
 Context:    default
 Debug Mode: false
 Plugins:
  buildx: Docker Buildx (Docker Inc.)
    Version:  v0.10.4
    Path:     /Users/nathan/.docker/cli-plugins/docker-buildx
  compose: Docker Compose (Docker Inc.)
    Version:  v2.17.3
    Path:     /Users/nathan/.docker/cli-plugins/docker-compose
  dev: Docker Dev Environments (Docker Inc.)
    Version:  v0.1.0
    Path:     /Users/nathan/.docker/cli-plugins/docker-dev
  extension: Manages Docker extensions (Docker Inc.)
    Version:  v0.2.19
    Path:     /Users/nathan/.docker/cli-plugins/docker-extension
  init: Creates Docker-related starter files for your project (Docker Inc.)
    Version:  v0.1.0-beta.4
    Path:     /Users/nathan/.docker/cli-plugins/docker-init
  sbom: View the packaged-based Software Bill Of Materials (SBOM) for an image (Anchore Inc.)
    Version:  0.6.0
    Path:     /Users/nathan/.docker/cli-plugins/docker-sbom
  scan: Docker Scan (Docker Inc.)
    Version:  v0.26.0
    Path:     /Users/nathan/.docker/cli-plugins/docker-scan
  scout: Command line tool for Docker Scout (Docker Inc.)
    Version:  v0.10.0
    Path:     /Users/nathan/.docker/cli-plugins/docker-scout

Server:
 Containers: 7
  Running: 4
  Paused: 0
  Stopped: 3
 Images: 69
 Server Version: 23.0.5
 Storage Driver: overlay2
  Backing Filesystem: extfs
  Supports d_type: true
  Using metacopy: false
  Native Overlay Diff: true
  userxattr: false
 Logging Driver: json-file
 Cgroup Driver: cgroupfs
 Cgroup Version: 2
 Plugins:
  Volume: local
  Network: bridge host ipvlan macvlan null overlay
  Log: awslogs fluentd gcplogs gelf journald json-file local logentries splunk syslog
 Swarm: inactive
 Runtimes: io.containerd.runc.v2 runc
 Default Runtime: runc
 Init Binary: docker-init
 containerd version: 2806fc1057397dbaeefbea0e4e17bddfbd388f38
 runc version: v1.1.5-0-gf19387a
 init version: de40ad0
 Security Options:
  seccomp
   Profile: builtin
  cgroupns
 Kernel Version: 5.15.49-linuxkit
 Operating System: Docker Desktop
 OSType: linux
 Architecture: x86_64
 CPUs: 4
 Total Memory: 5.804GiB
 Name: docker-desktop
 ID: dc980d43-b287-4b8d-90b1-992be4c7b457
 Docker Root Dir: /var/lib/docker
 Debug Mode: false
 HTTP Proxy: http.docker.internal:3128
 HTTPS Proxy: http.docker.internal:3128
 No Proxy: hubproxy.docker.internal
 Registry: https://index.docker.io/v1/
 Experimental: false
 Insecure Registries:
  hubproxy.docker.internal:5555
  127.0.0.0/8
 Live Restore Enabled: false

Anything else?

No response

Start by reproducing the issue with the provided docker-compose.yml and docker compose up --wait, then trace the up --wait entry point handling a successfully completed init container with no dependents. Done means the command returns exit code 0 for this case, with a regression test covering the behavior.