This is indeed a good example.
I think what you are looking for in GIMP is the Heal tool[1]. It sounds a bit like the xyproblem[2,3]: what you want is a way to erase part of the picture, not "the clone/stamp brush in GIMP". It may also be related to the "curse of knowledge" cognitive bias, but you have to unlearn some of what you already know (and doesn't apply here): having a different interface is supposed to help a bit here.
I understand why you'd just want "photoshop but free", but there are a lot of reasons why it would be complicated to obtain, if achievable, not to mention... desirable?
Regarding the heal tool, on my UI (2.10.34) I have to long-press the "clone" button, next to the eraser, to get it. Now that I mention it... the "clone" tool [4] may be what you are looking for? I tend to prefer the heal tool though. The "clone" tool was here since ~2004-2007 (timespan of the 2.2 version) according to the manual[5], which makes me question your memory, though.
Krita is more of a painting program than an image editor, so this tool is less needed. I am also less comfortable with it, but I found the "smart patch tool" [6] in under 30s of looking up "krita remove part image" in DuckDuckGo. I also found references to the clone brush, so I looked for it, that sounds more like what you describe[7].
Anyway, I don't want to attack you or anything, I would just like to point out that in general, when switching tools, it's better to look for the idiomatic way of achieving the same result, than a 1:1 equivalent of every step.
[1]: https://docs.gimp.org/en/gimp-tool-heal.html
[2]: https://en.wikipedia.org/wiki/XY_problem
[3]: https://xyproblem.info/
[4]: https://docs.gimp.org/en/gimp-tool-clone.html
[5]: https://docs.gimp.org/2.2/en/gimp-tool-clone.html
[6]: https://docs.krita.org/en/reference_manual/tools/smart_patch...
[7]: https://graphicdesign.stackexchange.com/a/124754