The core of the issue lies with bind mounted volumes. Previously, docker desktop had elevated privileges / permissions but now after shifting over to colima, the same privileges were no longer there.
User permissions weren't being passed on properly to the containers, resulting in them being unable to access the binded volumes on the host machine. The solution is to add a user:group or uid:gid mapping in the docker run command or the docker-compose file etc.
user: "<uid>:<gid>"
In a docker-compose file, it would look like this: