OK, I have found a solution ... you have to download the standalone application (Music Manager) to your PC through which you can upload and then play music on Google Play interface in Opera.
The problem in Opera is that while it supports Chrome extensions, it doesn't support Chrome applications. That's the problem. Therefore you have to use the Music Manager.
I hope that Opera will come up soon with support of Chrome applications!
I've been getting the same thing with 12.14. Would be nice to have it working again, with some work around or what have you. But no skin off my nose if on fix or work around is found, as I seldom use it. But would be nice for it to work when I do.