Little planet is a plugin that allows you to take a 360 panorama (or ideally a photosphere) and warp it so it looks like a little planet. A long time ago, around 2008ish, I was using software like autopano and hugin to stitch together photospheres and then some process to turn those into little planets.
It definitely wasn't the "little planet" plugin, I'm pretty sure it was in gimp, possibly in script-fu but I don't remember for sure and so far googling has brought up nothing.

The main difference between the current little planet plugin and this other thing (or at least the feature I'm looking for) was the ability to "pinch" the image at the same time, so the radius of the planet would shrink but features towards the edge, such as buildings on the planet would stretch and become relatively larger. I can produce a similar effect using the pinch plugin, but that takes a lot of faff to avoid ending up with oval shaped planets and the overall effect isn't quite as good.

Anyone any idea what I'm talking about?

If you have the gimp_gmic_qt plugin installed, www.gmic.eu A filter in the Deformations section Stereographic Projection

Some screenshots of that one here: https://inouetetsurou.wordpress.com/202 ... %E3%82%8B/

For stitching? I still have an old 32bit AutoPanoGiga working in linux but a newcomer, xpano is very good https://github.com/krupkat/xpano - versions for all platforms

In gimp under filters - render there is also sphere designer

Do you mean this one?