I noticed that nextcloud was out of date again. I thought my previous update attempt based on this SO answer would do the trick, but it was missing a step.

docker-compose -f /path/to/docker-compose.yml stop
docker-compose -f /path/to/docker-compose.yml pull
docker-compose -f /path/to/docker-compose.yml up --force-recreate --build -d
docker image prune -f

Of course, I have some of this wrapped in systemd.service files, so this really ends up looking like:

sudo systemctl stop my.service
# Edit this file if wanting to upgrade major version (currently nextcloud:21-fpm-alpine)
vim /path/to/docker-compose.yml
docker-compose -f /path/to/docker-compose.yml pull
sudo systemctl start my.service
docker image prune -f

Go here to find available version tags: https://hub.docker.com/_/nextcloud