The symptoms here sound very much like https://bugs.launchpad.net/ubuntu/+source/gdebi/+bug/1854588 which has now been fixed in Ubuntu, but not submitted to Debian
There was also a fix drafted in https://salsa.debian.org/atzlinux-guest/gdebi/-/commit/1de6b00bef539de4458021dc02ed2110f76ab630 but not record if it worked. It wasn't uploaded to Debian. I think the root cause why gdebi is broken is that it is unmaintained. Looking at https://tracker.debian.org/pkg/gdebi the source code hosting points to https://code.launchpad.net/~gdebi-developers/gdebi/trunk. Last version in this source code was 0.9.5.7 in 2015, followed by commit that source code moved to https://code.launchpad.net/~gdebi-developers/gdebi/+git/main in 2022, yet that location has zero new commits since the 0.9.5.7 in 2015. If it was maintained, and there was a git repository people could contribute to, many of these bugs would have been fixed. Currently it is just maintainers doing one-off emergency fixes without storing anything in git in a way that would allow for contributions from users like Doug Brown in LP#1854588.
