It appears that the only valid solution to this situation is to downgrade Eclipse to a lower version.

In my case, I tried debugging Java 1.6 code on Eclipse 2024-03 R, and I also tried applying solution presented in Eclipse Community forum: https://www.eclipse.org/forums/index.php/t/1112744/

However, nothing worked until I downgraded Eclipse to version 2020-12. I suppose other (a little bit newer) versions could also work, but this one is working for me.