Hi liquidnonsense.
Given the steps you've already taken including deleting and reinstalling GarageBand and the fact that the error messages you're seeing point to a disconnect of some kind at the basic open-and-save level of the OS, I'd advise going deeper and actually reinstalling macOS Mojave. You've not specifically said that the issue began after the latest update, but given the timing, I'd bet that's the case.
You can reinstall macOS "in place" without a high probability of data loss. That said, a good Time Machine backup is always a user's best friend in a situation like this. If you're not already using or are not familiar with Time Machine, check here:
Time Machine - Apple Support
When you reinstall macOS Mojave, you'll do it from Recovery Mode. Again, if that is not a familiar process, you can find step-by-step guidance here:
How to reinstall macOS from macOS Recovery - Apple Support
Cheers.