Just to clarify: most people (myself included) don’t actually do this. See Project.toml [compat] best practice: should I manually remove incompatible old dependency versions?
In your case, I was just suggesting that your stated compatibilities are unusually broad, so you should actually verify them (at least manually, if not by CI).
What most people do, and what is probably the right solution for you as well: When you’re registering your new package, set the compat entry for all of your dependencies to the x.y that is the most recent release for that dependency. This means that your package will require that dependency version as a minimum, and also accept any future releases of the dependency that are not breaking according to semantic versioning (so all 0.y.* versions and all x.*.* version for x > 0).
When you make new releases of your packages in the future, verify that the compat entry for all your dependencies is still ok (that is, your package still works with the given minimum version). If not, update the compat entries to the most current release of your dependency.