For the downloaded debs, you can install them using:
1.sudo dpkg -i ~/Downloads/<packagename.deb> or
2. sudo dpkg -i and then open the Downloads folder, select a deb and drag it into the terminal and the path will autopopulate.
For Edge, I suspect it will block other files, not just debs. It just happened to be that you noticed it first with debs. Likely something in its download or security settings. You may want to ask on an Edge forum as well about this issue.