I have a laptop and a Desktop that both run Debian 10. On the Desktop the situation is that in the Subject of this post [Google Earth in Debian GNU/Linux 10 (buster) renders as small square upper left in Gnome Classic and Xorg, but properly full-window in Gnome (Wayland)]. On the laptop, Gnome Classic runs GE nicely (as well as Gnome), whereas Gnome Xorg generates the little square in the top left of the screen. GE version is Google Earth Pro 7.3.3.7721 (64-bit) in both cases.

The preference would be the situation of the laptop, in the desktop. The desktop is much faster than the laptop and is newer. Gnome by itself, which is really Wayland, is a bit halting with the mouse and every now and then crashes on something. How it crashes: One of the dual screens becomes erratic, then the whole display becomes unreadable. It becomes impossible to logout or reboot. GE seems to hog time on the desktop in Wayland, perhaps leading to these crashes. I find myself wondering if I chose different architectures (amd64 or i386) of Debian to install on the two machines when I installed the image files, if they treat the GUI systems differently. Or perhaps the problem is in the CPU (Intel on the Desktop, AMD on the laptop) that is running. Or maybe GPU's treat Wayland differently. What seems clear is that GE Pro needs Wayland to run these days. The old Xorg is not sufficient anymore.

GE Pro "About Google Earth" lists:

Build Date Tuesday, May 26, 2020 6:41:18 PM UTC
Renderer OpenGL
Operating System Linux (4.19.0.0)
Graphics Driver nouveau
Maximum Texture Size 8192×8192
Available Video Memory information not available
Server kh.google.com

The Desktop Settings lists the following information:
Debian GNU/Linux 10 (buster)
Memory: 23.5 GiB
Processor: Intel® Core™ i5-7400 CPU @ 3.00GHz × 4
Graphics: NVA8
GNOME: 3.30.2
OS Type: 64-bit
Disk: 1.3 TB

The laptop lists in Settings:
Debian GNU/Linux 10 (buster)
Memory: 11.3 GiB
Processor: AMD® E-300 apu with radeon(tm) hd graphics × 2
Graphics: AMD® Palm
GNOME: 3.30.2
OS type: 64-bit
Disk: 487.4 GB