I have just moved to Debian Testing (Buster) and am unable to get Avidemux to run on it. I have tried both the appIMage and the tar.gz of 2.7.2. Avidemux ran well on Debian 9 (Stretch).
By "I have tried [...] the tar.gz" do you mean that you successfully compiled (and eventually installed) Avidemux on Buster, but avidemux3_qt5 doesn't run? Please post the terminal output from an attempt to execute avidemux3_qt5 (or the wrapper script for portable mode, if you try to run it without installation).
I'm afraid I got tired and gave up. I shall download the appImage again.
[Inexplicable success] I downloaded the 2.7.2 appImage again and did with it exactly what I had done earlier. And this time it worked. I cannot explain this.