The real question is - if EAGLE installer does not work - why EAGLE version 9 no longer have Linux repository - it did in version 3 ...
You would have to ask Autodesk about that.
A little Googling found this page
... where a jorge.garcia from Autodesk says in part
I hope you're doing well. Currently, the linux version of EAGLE doesn't have an installer so once you extract the tarball, just cd into the extract folder and type ./eagle to start EAGLE.
We are working on restoring a formal installer to EAGLE on the linux platform and that will be available very soon.
Mind you, that was on 11-15-2017, nearly 4 years ago
Other than that, you have to go through the hoops of running it from Terminal, unless you build a .desktop file eg eagle.desktop and then that can act as a launcher from either your desktop or your dock. If you wish to explore that option, ask about it here.
I can, however confirm that the details linked to by @TheProf
at your other thread, namely here
... do indeed work, I have just confirmed that on this Ubuntu 20.04 GNOME I am running currently (similar enough to your 21.04), but I just went as far as the sign in popup and have not created an account.
I am going to lock your other Thread and link to here, as this is more current.