From what I can tell, the options to get an Amazon Music player running under Linux is limited with the end of support announcement from Nuvola Player at the end of 2022. Plus, I have not been able to get Nuvola working with Ubuntu 20.04. One quick fix to try in Linux is a user agent switcher.
If you are like me, you visit the music.amazon.com site with Firefox only to be told the version is not supported and you need to upgrade to the latest version. The only problem is the latest FF for Linux is installed. Working in Cybersecurity I know there is a fake out for sites checking for specific versions of a browser when the browser agent version is requested. In Firefox it is a simple search for the User-Agent Switcher extension and installing it. Once installed, navigate to Amazon Music and get the notice about the wrong version of a browser. Now, left click on the browser agent switcher extension icon and choose Windows and Firefox. Now refresh the Amazon Music web page and you should be able to play music in Amazon Music. Firefox may prompt with a banner at the top of the web page window about accepting DRM to visit the site and Firefox may also perform a configuration change or update the first time you try stream. I think it’s more of the the OS version the agent switcher is providing versus the version to get it working. Amazon may figure this workaround out and make some other change to break it in the future, but it works for now. Update: This worked for a few days before Amazon made an update to the browser version. So, I found another extension for user agent spoofing. It is has a more more icon driven interface and is not quite as configurable for which sites need a specific user agent returned, but it’s working today, but I have found Amazon will remember previous visits and error out but using private or incognito browser sessions usually work. If you need guidance, here is a YouTube review that should show how works.