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to gradle.build, then Gradle will download that version and use it in the IDE, and code against that specific version, what if version 3.5 has some new interfaces or new method signatures, you will not be using the correct version, or the version that has the "improved" method...

There is no "correct" version.
There is a compile time version and a runtime version. Most of the time you want the highest runtime version possible. But you change the compile time version only when you really need to.

Lets say you have a compile time depency to a module in version 3.0.5. It's actually the most current version when you start developing. You have all the interfaces you need, implement your module and it works. Now, you deploy it on the production server.

But in the meantime, it was patched it is already on version 3.2.0. And later on, the server is patched again and the version of the module increases to 3.3.14

That's good. Since there was no major version increment, the interfaces were not changed in an incompatible manner. Everything is fine. Your module still compiles and works as intended. You could, of course update your dependency version to the most current version, but why bother?

But let's say, a few months later you have a new requirement and you find a superuseful method in the documentation. But it isn't there when you start implementing. You find out that it was added in version 3.5. That's bad. You can of course update your dependency in the IDE, but your module won't deploy. It needs version 3.5, but only 3.3.14 is provided. So you need to patch your server to at least patch 60. Since there is already patch 70, you patch it to 70.

Now you update the compile time version to 3.5 since the interface you need is there in that version. You could try to find the exact version of the deployed module, sure. But why bother. With the next patch, it will increase again.

And in fact you say "if the interface changes" , maybe I'm missing something, but where do you check if a specific core bundle got an important change? (git source repo?) sounds like much manual and time consuming work...

Nobody tracks all changes to all methods and all classes. Nobody cares. When you have a requirement, you check, if there is a method that might help, but otherwise, you simply don't track all changes. It's too much work.