Mongo Express to wait for MongoDB Cluster in Docker Compose - mongodb

Question

I'm trying to setup a local development with Docker Compose that has a MongoDB cluster as the database. I chose Mongo Express as the Database Admin User Interface so I can check inside the MongoDB database. It does take some time for the cluster to accept connections, I have the 3 db containers as part of the depends_on, but seems like I have to do more than that based on the Docker Compose documentation here. I can't seem to find a good example for waiting for MongoDB clusters. Has anyone figured this out already? Please share, that would be great. Thank you in advance!
Here's the docker-compose.yml file:
version: '3.9'
services:
mongodb-primary:
image: 'bitnami/mongodb:latest'
environment:
- MONGODB_ADVERTISED_HOSTNAME=mongodb-primary
- MONGODB_REPLICA_SET_MODE=primary
- MONGODB_ROOT_PASSWORD=password
- MONGODB_REPLICA_SET_KEY=replicasetkey
volumes:
- 'mongodb_master_data:/bitnami'
mongodb-secondary:
image: 'bitnami/mongodb:latest'
depends_on:
- mongodb-primary
environment:
- MONGODB_ADVERTISED_HOSTNAME=mongodb-secondary
- MONGODB_REPLICA_SET_MODE=secondary
- MONGODB_INITIAL_PRIMARY_HOST=mongodb-primary
- MONGODB_INITIAL_PRIMARY_PORT_NUMBER=27017
- MONGODB_INITIAL_PRIMARY_ROOT_PASSWORD=password
- MONGODB_REPLICA_SET_KEY=replicasetkey
mongodb-arbiter:
image: 'bitnami/mongodb:latest'
depends_on:
- mongodb-primary
environment:
- MONGODB_ADVERTISED_HOSTNAME=mongodb-arbiter
- MONGODB_REPLICA_SET_MODE=arbiter
- MONGODB_INITIAL_PRIMARY_HOST=mongodb-primary
- MONGODB_INITIAL_PRIMARY_PORT_NUMBER=27017
- MONGODB_INITIAL_PRIMARY_ROOT_PASSWORD=password
- MONGODB_REPLICA_SET_KEY=replicasetkey
dbadmin:
image: mongo-express
restart: always
ports:
- 8081:8081
depends_on:
- mongodb-primary
- mongodb-secondary
- mongodb-arbiter
environment:
ME_CONFIG_MONGODB_URL: mongodb://root:password#mongodb-primary:27017,mongodb-secondary:27017,mongodb-arbiter:27017?replicaSet=replicaset
ME_CONFIG_BASICAUTH_USERNAME: admin
ME_CONFIG_BASICAUTH_PASSWORD: mexpress
volumes:
mongodb_master_data:
driver: local