automake: Remove distcheck hack

This was verifying that the autotools build would produce a
meson-buildable tarball. That was fine for 1.20 but going forward we
should switch to using meson's dist target for the release tarball.
3 jobs for remove-distcheck-hack in 4 minutes and 31 seconds (queued for 66 minutes and 45 seconds)
latest
Status Job ID Name Coverage
  Docker Image
passed debian-testing #137690

00:00:31

 
  Build And Test
passed autotools-build-and-test #137691

00:02:47

passed meson-build-and-test #137692

00:01:12