My Laptop has 2 problems

Some HP Envy models have a bug in their UEFI (BIOS) Firmware.

Please open Windows security center (Windows Defender) and check if "core isolation" is enabled. If so disable this, reboot and see if you can now shutdown the Laptop properly.

I had the same problem with my Envy 13 X360 13-ar0004ng. After a certain version the official HP UEFI firmware updates broke the classic standby (S3 suspend to ram) and had bugs in the ACPI table. Now only modern standby works and if you enable core isolation the laptop does not properly shutdown, suspend or hibernate. Instead it crashes and restarts. This was not resolved in in newer updates and there will be no future UEFI updates from HP. Disabling core isolation (while being slightly less secure) solved the issue for me.

For the camera - many Envy laptops have a physical camera switch to disable the camera for privacy reasons. Check if the camera is listed and visible in Windows device manager and has a working driver. Windows comes with basic camera drivers that should work. Check the position of the camera switch. If you have dropped the laptop there is a chance the casing got slightly bent and the plastic outer switch part got dislodged and does not move the internal switch on the mainboard correctly anymore. (This happend with my Envy 13). The solution is to open the side of the case, refit both switch parts and carefully bend the case back a bit if it has a curve from being dropped.