You can test the current version of Opera without interfering with your normal Opera. Download the installer, launch it, click "options", set "install path" to a folder named "Opera Test" on your desktop, set "install for" to "standalone installation", uncheck "import data from default browser", and install.
Test in that Opera to see if you like it.
Further, if you do like it, you can test how upgrading from 58 is going to work out with your old Opera profile. In both Operas, goto the URL opera://about and take note of the "profile" path. Then, close both Operas. Then, in the test Opera profile folder, delete all files and folders. Then, copy all files and folders from your normal Opera profile folder to the test Opera profile folder. Then, you can test your old profile with the test Opera to see if everything is good to go.
If you use Opera Sync and want to take an extra measure of precaution, you can back up a few things first.
Goto the URL opera://settings/passwords, click the 3 vertical dots to the right of "saved passwords" and save your passwords to a csv file.
Right-click on an open tab and choose "save all tabs to a speed dial folder".
Goto the URL opera://bookmarks and use the drop-down to export your bookmarks to an html file. You can then delete the speed dial folder you created and empty the bookmark trash if you want.
Copy the "Bookmarks" and "Bookmarks Extra" files in your Opera profile folder to a safe place along with your password csv file and bookmarks html file.
Then, if you decide everything is good, you can upgrade your Opera 58. Just for good measure, make a copy of its profile folder while Opera is closed. If you don't want to upgrade, then no harm done.
@nunya Most probably those sites didn't update their media players, they should have been using HTML5 since a long time but sending the Flash based players to Opera.
Since now Chromium seems to send info that there's no Flash support, those sites started sending the HTML5 based videos to Opera.