Before posting I actually deleted a file and went to the web interface to check but couldn't find anything looking like that feature. I know they basically have a git like file management, but thought they just didn't expose past deleted files (clicking on the events timeline just moves to the folder the file belonged without any further information).

For anyone making the same mistake, the trashcan left to the search box in the action bar, it's not to delete stuff, like it does in the OSX Finder bar. It's to show past deleted files in the current folder (they then appear grayed out in the listing).

Fairly OT, but even knowing what the icon does, the is a thrill going to my spine when clicking this trash icon. But to be fair, the image is not wrong, it's just the habit of the OSX Finder.