When you purchase an app, you buy it for the device model and the system it has been built for. You can use the app, as long as you have a compatible device and a compatible system. A major system upgrade is creating a new world which older apps have not been prepared for, and It is not to be expected, that all older application or device drivers will be able to run any longer, when you upgrade the system on a device to a new, completely redesigned system version.
Before you upgrade to a newer system version, you should check your software, if it will be compatible with the new system version. You are not forced to upgrade to a new, major release, unless you need to buy a new Mac, that will only come with the current system version or you are eager to use the new, improved features of the new system version, but then the price to pay will be to find updated versions of older apps and drivers that will no longer be able to run.