Hello, Kai ! My name is Clement, and I've made the Apptainer for LANDIS-II linux on Github.
I'll be happy to help if I can.
For Singularity : Apptainer is simply the program Singularity that has been renamed "Apptainer" more recently. So if you have Singularity on your linux server, if might be the same program but in an older version.
As for not being able to run the build runscript, I'll need a bit more information on that. What do you mean by runscript ? Can you write down the command(s) that you've been using, and copy/paste the error that you're getting from them ?