Did a bit of experimentation, using weekly LiveUSB build of Testing (KDE flavor) from 2025-05-12 and booting into it on three different machines. The environment has been kept as-is, only updating mandatory dependencies during labplot installation.
In all cases the native version installed from Testing/Unstable repos segfaulted instantly in the same way. However, Flatpak and AppImage builds of labplot-2.12 launch and work without any problems, as intended.