Safe ways to specify postgres parameters for healthchecks in docker compose

I'm using secrets to manage username, password, and dbname with a Docker stack using Postgres as a DB. I now want to use the healthcheck feature that Docker provides.

docker-compose.yml:

x-db-secrets: &db_secrets
    - psql_user
    - psql_pass
    - psql_dbname

services:
  db:
    image: postgres:13.1
    volumes:
      - postgres_data:/var/lib/postgresql/data/
    environment:
      - POSTGRES_USER_FILE=/run/secrets/psql_user
      - POSTGRES_DB_FILE=/run/secrets/psql_dbname
      - POSTGRES_PASSWORD_FILE=/run/secrets/psql_pass
    secrets: *db_secrets
    healthcheck:
      test: pg_isready -U myuser -d db_prod
      interval: 10s
      timeout: 3s
      retries: 3

(... other services...)

volumes:
  postgres_data:
  static_content:
  media_content:

secrets:
  psql_user:
    external: true
  psql_pass:
    external: true
  psql_dbname:
    external: true

As can be noted in the healthcheck: section, I'm exposing the db username & the dbname with the healthcheck. My question (with some follow-up based on the answer):

• Does it matter? The docker-compose.yml file doesn't live on the host where this code will run. Therefore a potential attacker wouldn't have access to this info from there... however, since docker will perform the healthcheck, it would possibly live traces in that container (shell? docker configs files where that procedure is stored?)
• If it does matter, how can I perform the healthchecks without exposing that information? I would have to use the secrets directly, however I cannot figure out how to use the secrets in the docker-compose file...

Thoughts? Workaround?

Additional details:

• I'm currently checking if the DB is up from the (flask) container that uses it. E.g. the flask service checks if it can ping the DB or not. However I'd rather compartmentalize things, and the DB container should be the one telling if it's healthy or not (imo).

POSTGRES_HOST=db
POSTGRES_USER=root
POSTGRES_PASSWORD=password
POSTGRES_DB=dev

services:
  db:
    image: postgres:13.1
    volumes:
      - postgres_data:/var/lib/postgresql/data/
    env_file:
      - .env
    secrets: *db_secrets
    healthcheck:
      test: ["CMD-SHELL", "sh -c 'pg_isready -U ${POSTGRES_USER} -d ${POSTGRES_DB}'"]
      interval: 10s
      timeout: 3s
      retries: 3