What are the major differences between the recommended 5.15 kernel and the latest non-experimental 5.19.13-1? Are there any performance advantages or better security? And what is the difference of 5.19.0_rt10-3 (Realtime) and the 5.19.13-1?
Kernels are for hardware support. Newer kernels allow you to use newer hardware. But newer kernels sometimes introduce new bugs with older hardware. Install the newer kernel if you want, and test it. I would recommend leaving the older LTS kernel in place. If you have problems with the newer kernel you can boot into the old one and remove the newer one. Besides its a good practice to have two kernels installed in case of bugs or bad upgrades.