On my postgresql docker image :

initdb: error: could not access directory "/home/postgres/pgdata/data": Permission denied

I reused a previous image

volumes:
  - pgsql_data:/data/pgsql
environment:
  PGDATA: /data/pgsql

So actions :

• start image without setting PGDATA, then execute :

Then :

docker exec myimage id # to check the user (here 1000:1000)
docker exec myimage ls -l /data/ # to check the mount directory
docker volume inspect pgsql_data # give the path of the volume
// update the rights 
chown 1000:1000 -R /home/docker/volumes/pgsql_data

• stop docker compose up pgsql
• restore PGDATA parameter
• restart docker compose up pgsql