XPS13 9360 media key control

Short version: For your specific case, it might be easiest to simply stop Chrome from responding to media keys, which you can do this way (at least as of the date on this guide): https://www.makeuseof.com/tag/stop-chrome-hijacking-media-keys-heres/

Long version: The issue you’re describing can arise with any given key or key combination that has a defined action in multiple applications that are open. I have this problem with Spotify and iTunes running simultaneously, since I keep iTunes always running so my phone can back up to my PC. I don’t know of a way to prioritize which applications receive key press notifications. I believe the application in the foreground might get priority if it’s actually an application that would respond to the key or key combination on question, but if all “eligible” applications are in the background, it might be based on the order in which the applications were launched. There might also be some API in Windows that allows an application to prioritize itself and only certain media applications might be coded to do that — which would then beg the question of what happens if multiple open media applications do that.