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Below are some very simple ways to verify the installed Gnome version on both Ubuntu, Debian and also on CentOS.
We will do everything by issuing a command in the terminal.

We run the terminal and give the commands:

For Ubuntu and Debian:

apt list --installed | grep gnome-desktop

A result that indicates our version of Gnome:

Gnome-desktop3-data/focal-updates,focal-updates,now 3.36.8-0ubuntu1 all [installed,automatically]
libgnome-desktop-3-19/focal-updates,now 3.36.8-0ubuntu1 amd64 [installed,automatically]

Which indicates the version 3.36.8

For CentOS systems:

issue the command:

rpm -qa | grep -i gnome-desktop

is the result:

gnome-desktop3-3.32.2-1.el8.x86_64 

Which indicates the version 3.32.2-1