When I tested in Dropbox before, I deleted from the 3-dot note menu and didn’t put any text in the body. I tried again with text in the body and deleted from the sidebar context menu but it still went to the trash. Mystifying!
I am doing this in my personal Dropbox, but I also have a work Dropbox on the same machine (I would t expect that to matter, but it’s a possible difference).
The settings for my personal Dropbox, in the Sync tab, at the bottom, say I’m “not eligible for the updated Dropbox for MacOS on File Provider at this time.” Maybe you’re on the updated one and it behaves differently with Obsidian for some reason?
I had this problem before Sonoma and I still have it. The same thing happened to me with iA Writer. Almost a year ago I spoke with the Dropbox developers (I was using a beta version) and in a new stable version it has been resolved with iA Writer but the same behavior continues with Obsdian. I will write again on the Dropbox forum…