I can't speak for other setups, but my NAS actually has its own recycle bin. I think it has to be explicitly enabled in settings when configuring the share drive.
I'll investigate this. I've been assigning network locations like //Whatever/ instead of drive designations. I suppose I need to make it a network attached drive.
Thanks for the point in the right direction, I've just learned something. I'll poke around a bit and see if I can manage this.
EDIT:
Since this isn't a NAS per-se, my options are limited. Deleted items on network shares, whether mapped as a drive or not, go poof for the most part.
I've done what this link has suggested and mapped a network drive on my desktop from the physical drive in my desktop then set a default user folder there (the useless to me "3D Objects" in my case) and it works correctly, an item deleted in Musicbee mapped to the new Z: drive rather than the //Whatever/ network location now goes to recycle bin.
The next step now is to test this method on my laptop.
EDIT2:
I've confirmed this working on my laptop now too. I've set the same network drive, and on this I used another of the Windows default folders relocated to the new Z: drive and the file in Musicbee now deletes and shows up in the Recycle Bin on both computers now. It appears the files are linked too as I can remove the file from the bin on either computer and it automatically stops showing on other.
This doesn't appear to be the most elegant solution but it works well enough.
Thank you for the point in the direction, I've learned something.