If I understand this correctly on mainline I am currently running ubuntu kernel 6.11.
I'd like to install the latest official ubuntu kernel available that is not mainline I guess since mainline is just kernel.org? How do I find this, and what would be the best way to install it.
I already have grub menu on boot to choose the version of kernel.
Ubuntu supplies security patches & updates only for supported kernels for a release.
An LTS release has kernel stack options, these are
GA or the initial kernel the release comes with; supported for the life of the product with security fixes applied when you perform updates
HWE or the hardware enablement kernel which comes from later releases; each kernel (from a non-LTS) is supported for six months before moving to the next, before the release settles on the GA kernel from the next-LTS release
OEM for specific hardware; Ubuntu Desktop and some ISOs will recognize certain hardware and install/use this if beneficial for the hardware detected during install.
You can of course change kernel stacks post-install, and multiple kernel stacks can co-exist on the install too (you select at grub which you'll boot with), however some closed-source kernel modules (eg. some NVIDIA drivers) can prevent multiple stacks from co-existing.
For details see https://wiki.ubuntu.com/Kernel/LTSEnablementStack
The newest/latest support HWE kernel for Ubuntu 22.04 LTS is 6.8; which was the GA kernel stack from Ubuntu 24.04 LTS.
If you install kernels from the Ubuntu Kernel team, ensure you read the support period as for security patching, as you'll discover rather quickly most are provided 'as is' with no security patches at all; ie. its safe to assume if you installed the kernel yourself (not from Ubuntu repository package) you took on the responsibility for applying security fixes too. The Ubuntu Kernel team provide their fixes via Ubuntu repository packages.