gdebi 0.9.5.7 on Debian 10.9 (x86-64) with Cinnamon 3.8.8, kernel 4.19.0-16-amd64, fresh download of Webmin (webmin_1.974_all.deb) from Sourceforge on a system that has never before had a Webmin install. Click Install Package button and gdebi silently exits without doing anything. I note that the Lintian Output window of gdebi is loaded with a couple hundred "unrecognized line" errors, I have tried a fresh download of Webmin with no change in behavior.
What if you try installing the .deb file from the terminal, with the
dpkg --installcommand?