In the kdeapps flatpak repository, there's an experimental Konsole flatpak that can be tested. It runs the host shell just fine, possibly because of https://invent.kde.org/packaging/flatpak-kde-applications/-/commit/3806b155aace455be639a2cf61d5be271ec24bdf. It cannot open new tabs with a different profile when I go to File -> New Tab -> select profile. This works with non-flatpak Konsole/Yakuake even under weird circumstances like those mentioned in https://bugs.kde.org/show_bug.cgi?id=468391 where I can run a different profile that runs distrobox.