Right now all home assistant releases on docker are tagged with the specific version, at the time of writing the last version would be 0.114.3.
Upgrading between major releases such as 0.113.x to 0.114.x is usually associated with some non backwards compatible changes, and therefore I would say that it’s not recommended to be done automatically - when I had this set up in the past I’d often come home from work and find something isn’t working, and requires manual fixing.
But upgrading between version 0.114.1 and 0.114.2 is generally considered safe, backwards compatible, usually contains bugfixes, which also might contain security fixes.
Right now when running home assistant core in a docker container there is no way to easily, automatically upgrade to all 0.114.x versions, but not 0.115.x or anything else, using common methods such as watchtower.
This could be solved by having one additional tag per version, in the 0.114.x release example the tag would be 0.114 - and the image would be updated whenever there’s a new 0.114.x release.
This is pretty common, and can be seen, among other repos, here for postgres https://hub.docker.com/_/postgres?tab=tags