What is the cause of my rear wheel wobble? bearings dead?

service your cup and cone bearings. And check if the axle is still intact with the QR removed.

you need two thin metal cup and cone wrenches and look up the parktool video on that.

With that much play chances are high you also need new balls and cones because of pitting. you should have adjusted them earlier to prevent that.

I have also seen broken axles like that which were just held together by the QR skewer. . – Thats dangerous, don’t ride until you fix it!

Axle breaking happens more often on freewheel equipped hubs prior to the invention of HG freehubs. Better get a new HG rear wheel in that case. but finding one with the correct width or changing the width of an axle is a whole other rabbithole.