SUMMARY
The Media player applet shows multimedia controls for applications that are not media players. In my case Element, an instant messenger client. Since the client is based on Electron and uses notification sounds, I suspect that the Media player applet notices this and reacts.
Media player applet then shows playback as paused. Clicking on it's buttons (back, pause/play, forward) doesn't do anything.

STEPS TO REPRODUCE
1. Start up KDE, launch Element
2. Receive a message notification in Element

OBSERVED RESULT
Media player applet shows up in system tray and stays there as long as Element runs.

EXPECTED RESULT
Media player applet doesn't do anything and stays hidden.

SOFTWARE/OS VERSIONS
Operating System: KDE neon 5.20
KDE Plasma Version: 5.20.3
KDE Frameworks Version: 5.76.0
Qt Version: 5.15.1
Kernel Version: 5.4.0-53-generic
OS Type: 64-bit
Processors: 4 × Intel® Core™ i7-3520M CPU @ 2.90GHz
Memory: 7,5 GiB of RAM
Graphics Processor: Mesa DRI Intel® HD Graphics 4000

ADDITIONAL INFORMATION
This has been happening for a long time now, it's not specific to this KDE version.
While this could be considered a bug of the Element application, a general white/blacklist of applications that the Media player plugin interacts with might be a good way to solve this.