I am unable to confirm if the r7 360 is supported by the amdgpu driver on Ubuntu 20.04. On the ubuntu wiki ot states R7, but not explicit model numbers. Some r7 are cgn 1st gen and others are cgn second gen.
1 Answers
Proprietary
Here is a list specifically with the R7 360 proprietary drivers:
Seeing that the support is there only for 12.04.4 LTS and 14.04.2, I would guess that it's the fglrx Catalyst driver, which is not compatible with modern-day versions of the Xorg Server.
amdgpu-pro
AMD official info about the amdgpu-pro driver:
https://www.amd.com/en/support/kb/release-notes/rn-prorad-lin-amdgpupro
I see these in the table:
AMD Radeon™ R7 240/250/250X/260/260X/350
AMD Radeon™ R9 360 Graphics
But I don't see R7 360

Open source radeon
Relying on the open source radeon driver, in my personal experience, is like a box of chocolate; you never know how good support you are getting out of it.
All I can tell from personal experience, that with the AMD FirePro W5130M unfortunately it seems to be useless. Programs crash to an extent that needs reboot, or don't even start with the radeon driver.
But trying out is for free. Maybe it goes better for you.
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