Can we update gnome-shell 3.38.4 to any? In Zorin os 16.2
Not if you want your system to be usable. The current configuration does not support gnome 4*. It would replace zorin packages with Ubuntu packages, if that, and most likely refuse to boot.
So it's unable to update to gnome 40 cause of the boot
No, that update isn't possible because it modifies dependencies, some of which are customized to include Zorin configurations that improve usability, compatibility and performance. Modifying the Zorin OS with Ubuntu packages WILL BREAK THE SYSTEM.
Ubuntu, mint, pop and a few others are running gnome 4*. Have a go at them if you can't wait. Updating to gnome 4* in Zorin will make it unusable, if it even boots.
I experienced this when i updated the kernel to 6.09 and I had to recover from backup. It installed gnome 42, REMOVING ALL OF THE ZORIN/ GNOME SYSTEM APPLICATIONS. I was unable to load a desktop and if i could, there were no system applications to run, let alone services that were necessary in order to interact with hardware.
It's not that it's unable to update is that if you update it, you change the dependencies and therefore will break your system.
My suggestion is to wait until Zorin OS 17 is released which will be in the second half of 2023 as that will have the updated packages using Ubuntu 22.04 as the base
The only real way for getting up-to-date Gnome shells is to go along with the Ubuntu release-schedules of in between versions of LTS-es.
Now that is Ubuntu 22.10 that has the latest, stable, Gnome-shell version at this moment. Ubuntu is NOT Zorin ...... so if you really like Zorin, just hold on to the release of version 17 that is build on Ubuntu 22.04 LTS.
Gnome-shell on 16.2 still gets the latest updates for the Core of Gnome.
Besides an amount of bug-fixes, Gnome does not really alter that much for calling it outdated on Z 16 now today.