I’m stuck at kernel version 5.10 regardless of whatever method I try (even despite linux search cmd I can’t get any newer kernel version). As additional information, I installed PureOS on my Librem 14 laptop (with Pureboot software) with two SSDs as a dual boot configuration with Qubes via a live USB just to test features initially. To be honest, I hope there will be a community guideline of how to upgrade kernels in this distro since I haven’t found anything close in PureOS (if I’m wrong, please send me the corresponding link).
The latest kernel for laptops available in PureOS Byzantium right now is 5.10.158, which has been released in December 2022. The same applies to Debian Bullseye, which Byzantium is tracking.
It is up to date - well, almost, since the latest 5.10 kernel upstream has been released last week. Debian will catch up eventually, and so will PureOS.