I for one never encountered this scaling before. As you say the Lazarus forum is very helpful.

MyIntegerVariableForScaling := Screen.PixelsPerInch;

Seems to do the trick. Though it took some time to remake the program. I wouldn't be surpised if I missed something too. But now the new scaling ready version is downloadable on my site.

Gameplay and appearance are supposed to remain unchanged.

It turned out the UI scaling is possible in Linux too. At least for the KDE Debian I use.

Haven't found that option on Raspberry but I guess most Raspberry users don't use High DPI monitor. And frankly I don't either.