Mint is based on Ubuntu, both of which are versioned release distributions. The idea behind versioned releases is that the kernel and a lot of the software are all chosen and tested to work well together. It gives the user a system that won’t change much for several years. Rather than getting the latest and greatest, you get a known, relatively static set that works smoothly and gets security/stability updates rather than big upgrades. Typically, distributions like Mint only get minor security updates to the chosen kernel during their lifetime. You’ll see additional patches to kernel 6.8, but nothing beyond that.
To get a newer kernel, the safest option is to wait until Mint 23 gets released and do a full upgrade to the new version of Mint. Along with the kernel, other pieces of the operating system will get a bump to much newer versions. Mint gives you the option to try newer kernels, but this is less stable and could break your system.
There are other types of Linux distributions that ship new versions of the kernel much more regularly. Rolling releases (to one extent or another) update the kernel and other software shortly after the new code is available and tested.
Stay away from Chromebooks. Even if you get a Chromebook that is reported to play well with Linux, there can be issues. I have/had two different Linux Chromebooks. They both had unique pitfalls.
I had an arm-based Chromebook that was actually the development target of a custom distro. At its best, it still required a fairly specific wifi dongle to work without kernel hacks. Even then, the processor was slooow and storage was a bit of a problem if I was using it for anything other than text editing.
I’m running an intel-based Chromebook these days with Arch. The biggest bottleneck is the built-in nonupgradeable storage (16gb). Most of my home folder is symlinked to an SD card that I keep in the slot at all times. It works well and has great battery life, but there are easier ways to play with linux on a laptop.