I have the same laptop, and while the BIOS/UEFI indeed doesn't activate any external monitors, Linux does it during boot before LUKS password prompt for me… not sure what the difference is? I'm on kernel 6.4.
There's also a firmware upgrade (the kind in /lib/firmware, not the kind in flash memory on the card) for the QCNFA765 wifi card that you have to install, which fixes both a lot (probably not all) of the s2idle issues, and gives a little bit of battery life. I found this out with some s0ix test tool that I now can't find… anyway, it should say in dmesg:
ath11k_pci 0000:01:00.0: fw_version 0x110b196e fw_build_timestamp 2022-12-22 12:54 fw_build_id WLAN.HSP.1.1-03125-QCAHSPSWPL_V1_V2_SILICONZ_LITE-3.6510.23
Also, as some siblings already posted, Insert is on Fn+F10, which does indeed suck… but funnily enough it is also (undocumented?) on Fn+E, where it was on previous HP Elitebooks. I find that slightly more useful due to being reachable one-handed…