Two things: You'd have to have ELEET set to start with Windows and apply a profile on startup to make it use software-applied settings every time you boot. Otherwise it will go back to just what you have set in BIOS. On that note, I think ELEET can do some helpful things for testing or OC-runs, but I wouldn't recommend trying to use that to control clocks on every boot. It has been quite buggy for me and many others, so I'd try to just stick with settings you can apply in BIOS.
 
Second, I'm not sure how much time they spent trying to put settings in for the non-top-sku CPUs. So if I had to guess (which is all it would be), they don't have the default specs quite right for your 13500...whether it's wrong in BIOS or the software, I don't know. You can put in a service ticket to try and get their attention as they don't seem to come on the forums very much anymore (except the warranty section). The 12th gen had ring clocks that were limited by the e-core speeds, but 13th gen fixed that. That said, I'm having trouble finding a specification for what the 13500 ring clock is supposed to be.