I'm pretty sure the driver you want is the free radeon driver. It explicitly supports your RV710 card according to Debian and according to the reports of Trisquel users on h-node, and Debian reports that the non-free amdgpu driver is for later video cards:
https://packages.debian.org/buster/xserver-xorg-video-radeon
https://h-node.org/videocards/view/en/904/Advanced-Micro-Devices--AMD--nee-ATI-RV710--Mobility-Radeon-HD-4300-4500-Series-
https://h-node.org/videocards/view/en/215/ATI-RV710--Radeon-HD-4550-
https://h-node.org/videocards/view/en/11/Advanced-Micro-Devices--AMD--nee-ATI-RV710--Radeon-HD-4350-

On Trisquel the package you need should be in the main repository and should be called xserver-xorg-video-ati:
https://wiki.debian.org/AtiHowTo
https://packages.debian.org/search?keywords=xserver-xorg-video-ati
https://mirror.fsf.org/trisquel/pool/main/x/xserver-xorg-video-ati/

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