Right, I missed the
--installed flag! Now I see:
$ apt list --installed | grep ^qt
qt5-default/focal,now 5.12.8+dfsg-0ubuntu1 amd64 [installed]
qt5-gtk-platformtheme/focal,now 5.12.8+dfsg-0ubuntu1 amd64 [installed,automatic]
qt5-qmake-bin/focal,now 5.12.8+dfsg-0ubuntu1 amd64 [installed,automatic]
qt5-qmake/focal,now 5.12.8+dfsg-0ubuntu1 amd64 [installed,automatic]
qtbase5-dev-tools/focal,now 5.12.8+dfsg-0ubuntu1 amd64 [installed,automatic]
qtbase5-dev/focal,now 5.12.8+dfsg-0ubuntu1 amd64 [installed]
qtchooser/focal,now 66-2build1 amd64 [installed,automatic]
qtdeclarative5-dev-tools/focal,now 5.12.8-0ubuntu1 amd64 [installed]
qtdeclarative5-test-plugin/now 5.9.5-0ubuntu1.1 amd64 [installed,local]
qttranslations5-l10n/focal,focal,now 5.12.8-0ubuntu1 all [installed,automatic]
but "make" still fails, just like before.