The big list under "Soplos Kernels" is pre-populated directly from our repository — those are prebuilt kernels available via apt, not something generated by a system update.

On Secure Boot: those prebuilt kernels from the "Soplos Kernels" tab aren't signed — no shim — so they won't boot with Secure Boot enabled. But as you mentioned, Soplos Kernel Installer also lets you compile your own kernel with MOK (Machine Owner Key) signing, and that does work with Secure Boot on. That's the path you already used when you manually built your "signed" kernel. So your options are: disable Secure Boot to use the prebuilt kernels, or keep compiling your own with MOK if you want to stay on Secure Boot.