I think you're mixing up some things. If you run the image "docker.io/wordpress:6.3.1", then the container will be updated when the image with that tag (6.3.1) is being re-built (which is a best practice, because that's the only way how you get security updates for the libraries in the base image). The tag is just a pointer to the latest image hash.
Many Docker images also provide "semantic version tags". Wordpress does too, so if you run the image "docker.io/wordpress:6.3", you will get the latest 6.3.x version.
It's up to you (and the image publisher) to decide when to auto-update, and when manual intervention is necessary.
Of course this requires trusting the publisher of that image. But even if you build your own images, you still trust the base image. It's turtles all the way down.