Drip is one of the better options if you want to just download something from your app store of choice. It’s FOSS, requires minimal permissions, and seems to store all data locally.

Wood glue is so effective because it soaks into the pores in the wood. This gives it a lot of surface area to hold the parts together. Wood filament isn’t nearly as porous as actual wood so wood glue won’t hold it as strongly.

Might work ok depending on what exactly you’re gluing but you’d probably be better off using 2 part epoxy.