Maybe there's a simple solution I missed but Is there an easy way to get my project files from the Bela board?

I know I can download individual files from the IDE but Ideally, I'd like to grab all my (30+) files at once to create a quick backup.

Is there a way to mount the internal filesystem to be visible over USB or ethernet?

Through the IDE you can download either the current project or all the projects:
have a look here

Ahh, thank you. I thought that button just downloaded the current file, like the button on the right. didn't think to try...sorry.