There’s clear performance differences between 6.1 and 6.6.3
As already stated, kernel 6.5 is available on Debian Stable.
Ofc, you can install newer kernels, you could install kernel 6.6.0 if you wanted, but you’d be going outside of the stable repo to do it which kinda defeats the entire purpose of Debian Stable.
No, it does not. Stable Backports exist for exactly this reason.
Not to mention that mixing and matching packages can lead to problems in the future. Like accidently using the wrong dkms driver version on the wrong kernel version.
I don’t know how you might have managed to do those things, but no, installing the Stable Backports kernel would not cause either of them.