My thoughts on the matter from when I was working a lot with Python: Inter-Release Versioning Recommendations - Michael Goerz
All of that still applies to Julia as well: basically, add a +dev or -dev suffix to the version number between tagged releases.
The one small refinement I’ve adopted is that I started to use -dev much more than +dev these days and use it to keep track of whether a pull request is major, minor, or bugfix: I’ll set the version to “whatever the version would be if this were released right now”, with the added -dev suffix. I might still use +dev if immediately after a release I’m fixing some typos in the documentation, or tweak a CI script, or something like that.