AMD Radeon 5600 - should be supported by kernel 5.6.0, which does not come with Zorin 15. However, the soon to be released Zorin 16 may well support it.
However, while the latest kernel includes a patch, the proper Graphics Drivers can be installed to run Radeon 5600M on Zorin 15, Ubuntu 18.04 or Ubuntu 20.04.
The downside is you would need to boot in
nomodeset to get installed. You would need to tolerate some low quality graphics until the installation is complete, then install the drivers.
As to why you had more luck with Manjaro and Arch- I suspect it is because they place more emphasis on included the drivers or higher kernels. For a broad audience, jumping to the latest and highest kernel can cause a lot of issues on older computers and many distros prefer to avoid that conflict.
To boot into nomodeset from you USB media, please see this guide here:
Unlike Nvidia, Radeon is supportive of open source and outsources their drivers.
Which is how they are included in the kernel. You may prefer to upgrade your kernel to the higher version after completing the install, rather than messing with the drivers.