I struggle to imagine doing so for anything but a personal side project

Don't imagine. You have any bash scripts your team uses? Rewrite them in Babashka. Start with your own personal scripts first, get a knack for it, feel the benefits (it's not going to be universally better for every case). You have to be very confident about it personally, because people will come for your guidance later.

This is a good strategy for introducing unfamiliar things - pick something less important, rewrite it, let it sit there. If it becomes problematic - easy to revert. If people start liking it, you can add more, and so on.

That's how I sneaked F# in my .net shop years ago - I started writing less important tests in it.