Sanity check on installed kernel packages

there was some past drama over kernel images and files that i think i have successfully resolved now, but wanted eyes on this output to help make sure everything is as it should be now.

apt list --installed linux-hwe* linux-image* linux-mod* linux-head*  linux-gen*
Listing... Done
linux-generic-hwe-22.04/jammy-updates,jammy-security,now 6.2.0.37.38~22.04.15 amd64 [installed]
linux-headers-6.2.0-35-generic/jammy-updates,jammy-security,now 6.2.0-35.35~22.04.1 amd64 [installed]
linux-headers-6.2.0-36-generic/jammy-updates,jammy-security,now 6.2.0-36.37~22.04.1 amd64 [installed,automatic]
linux-headers-6.2.0-37-generic/jammy-updates,jammy-security,now 6.2.0-37.38~22.04.1 amd64 [installed,automatic]
linux-headers-generic-hwe-22.04/jammy-updates,jammy-security,now 6.2.0.37.38~22.04.15 amd64 [installed,automatic]
linux-hwe-6.2-headers-6.2.0-35/jammy-updates,jammy-updates,jammy-security,jammy-security,now 6.2.0-35.35~22.04.1 all [installed,automatic]
linux-hwe-6.2-headers-6.2.0-36/jammy-updates,jammy-updates,jammy-security,jammy-security,now 6.2.0-36.37~22.04.1 all [installed,automatic]
linux-hwe-6.2-headers-6.2.0-37/jammy-updates,jammy-updates,jammy-security,jammy-security,now 6.2.0-37.38~22.04.1 all [installed,automatic]
linux-image-6.2.0-36-generic/jammy-updates,jammy-security,now 6.2.0-36.37~22.04.1 amd64 [installed,automatic]
linux-image-6.2.0-37-generic/jammy-updates,jammy-security,now 6.2.0-37.38~22.04.1 amd64 [installed,automatic]
linux-image-generic-hwe-22.04/jammy-updates,jammy-security,now 6.2.0.37.38~22.04.15 amd64 [installed,automatic]
linux-modules-6.2.0-36-generic/jammy-updates,jammy-security,now 6.2.0-36.37~22.04.1 amd64 [installed,automatic]
linux-modules-6.2.0-37-generic/jammy-updates,jammy-security,now 6.2.0-37.38~22.04.1 amd64 [installed,automatic]
linux-modules-extra-6.2.0-36-generic/jammy-updates,jammy-security,now 6.2.0-36.37~22.04.1 amd64 [installed,automatic]
linux-modules-extra-6.2.0-37-generic/jammy-updates,jammy-security,now 6.2.0-37.38~22.04.1 amd64 [installed,automatic]


note that the 35-generic kernel has been purged but the header remains because (i think) is it not marked as automatic… this is probably a holdover from me having to manually install it back during the drama.

also i think i manually reinstalled linux-generic-hwe-22.04 as well after accidentally removing it.

so my questions are:

  1. should i remove the 35-generic header and then run sudo apt autoremove to clear out the remnants?

  2. should i apt-mark the linux-generic-hwe-22.04 package as automatic, or does that matter?