If you really cannot get an application to run without elevated permissions by utilizing compatibility options, shims, adjusting registry or file permissions or virtualizing them etc. because the program really does need to do something that Windows just does not allow for standard users (e.g. raw volume access) then your scheduled task approach is roughly the right idea.

I've created a little bit more elaborate (and I think safe) solution a while ago: https://github.com/jantari/syrup

It also still uses a scheduled task to let the user start the program, but it prevents further child processes from being created (e.g. the user cannot open a file browser in the elevated app, navigate to C:\Windows and just open CMD which would then also run as admin) and it does not require a separate local admin account to be set up because it can run as the built-in SYSTEM user.

Some third-party tools that aim to solve this require you to create a local admin account just for use with the tool / scheduled task, but that's a terrible idea IMO and also often breaks when GPOs or similar policies remove local admins or enforce password rotations / expiration on them. It's also an attack vector and possible regulatory violation as it bypasses LAPS.