@MrTeatime I don't know if this is exactly what you're looking for, but I believe there is a way to have the persistent media player. When you open the media player tab, you'll see the options at the toolbar. There's one that's a rectangle docked to a square, and when hovered on, it says 'pin to toolbar'.

Selecting that will dock the player to your toolbar, and I've had it up for a couple days now. Admittedly, I haven't closed Opera since I attached it, but I have stopped and started listening to music over the course of several different sessions.

I hope that this helps!