Dragging folders from Box Drive into Bridge 2024 removes them from Box Drive

Sounds to me that this is no different from DropBox or OneDrive.

Each of the latter two (since I've never used Box Drive, I cannot say for sure on that one, but I strongly believe it's the same thing) has a folder on your system. At any time since the Mac first came out, if you moved files from one folder to another, it moved them, not copied them. But, also, since the Mac came out, if you pressed the Option key, you could copy them from one folder to another. 

Yes, Box Drive is a cloud service, but the folders on your computer do not care what is linked to those folders in the cloud; it just sees content in the folder that's on the computer. 

With DropBox, which I have the most experience with, if I drag a file out of a shared folder on my Mac, a window pops up asking if I really want to remove this file for everyone else. If I'm the sole owner of that folder, I do not get asked that question. This message comes from the DropBox software, not my Mac.

I suppose what you need to do if you want to remove a folder or the content(s) of a folder from Box Drive but do not want to remove those items from the cloud, press the Option key to make a copy of the files onto the new location on your hard drive. Then, you will have two copies of those files: those in Box Drive and those somewhere else on your computer. FWIW. I am always going into files in DropBox, using them, updating them, etc. I never thought to remove them from DropBox to work on them and then return them to DropBox. 

So, in short, if I'm correct, there's nothing to be addressed, it's working normally. 

If I'm wrong, please let me know.