Thanks everyone for helping with my Firefox issue ("sites should not be able to run anything unless they are open in a tab")!
My conclusion for the Firefox home showing a notification counter for Youtube is still unclear; it could have simply taken this from a title bar text (which would be fine); but I can't reproduce it right now for some reason. Ah well.
But the general concept of "code running while site is not opened" is a thing, and is happening through "service workers", as I learned from @desolationpark (thanks!)
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Here's some info on that: ghacks.net/2016/03/02/manage-service-workers-in-firefox-and-chrome/
"Service Workers are an up and coming feature [this article was written in 2016.. -red] supported by most modern browsers that enable sites and services to interact with the browser without having to be open in it.
Think of them as on-demand processes that enable the use of push notifications and data synchronization, or make sites work offline.
Web browsers are not designed currently to prompt users all the time when Service Workers are registered in the browser. This happens as a background process most of the time currently. (..) This is not made clear to the user as it happens in the background.
Chrome and Firefox offer no clear information on how to manage Service Workers that were added to the browser previously. While capabilities exist, they are more or less hidden from users at this point in time which is problematic if previously registered workers need to be removed from the browser.
This guide provides you with the means to manage workers in Firefox and Chrome."
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Tl;dr from this guide, for Firefox:
Go to "about:serviceworkers" to manage these processes;
Or it can be fully disabled: (I'm sure there's downsides to that; I'll find out soon enough 
)
Go to about:config
Find "dom.serviceWorkers.enabled" and set it to "false"
Yay! Feels good to no longer have invisible background processes running without my permission! 
Thanks everyone!
![From an end user's perspective, what can a mobile app do that a pwa web app with service workers can not do?
For most everyday tasks, a PWA with service workers can offer an experience very similar to a mobile app. However, there are still some things a mobile app can do that might be noticeable to an end user:
Deeper device features: Mobile apps can feel more integrated with your phone. For example, a photo editing app might be able to access all your photos directly, while a PWA might require you to upload them each time. Similarly, a fitness app might be able to track your location more seamlessly in the background compared to a PWA.
Always-on background tasks: Some mobile apps can perform actions in the background even when you're not actively using them. For instance, a music streaming app might continue playing music uninterrupted even if you switch to another app. PWAs with service workers can do some background tasks, but they might be more limited or paused to conserve battery.
App Store discovery and installation: Finding and installing mobile apps is usually a smoother process. You can browse app stores with categories and recommendations, and installation typically involves a single click. PWAs rely on users finding the website and then adding them to the home screen, which can be less intuitive.
[...] For many web browsing tasks or simpler functions, a PWA can offer a very similar experience to a mobile app.](https://files.mastodon.online/media_attachments/files/112/484/943/636/028/859/original/a1201346cb02225a.png "From an end user's perspective, what can a mobile app do that a pwa web app with service workers can not do?
For most everyday tasks, a PWA with service workers can offer an experience very similar to a mobile app. However, there are still some things a mobile app can do that might be noticeable to an end user:
Deeper device features: Mobile apps can feel more integrated with your phone. For example, a photo editing app might be able to access all your photos directly, while a PWA might require you to upload them each time. Similarly, a fitness app might be able to track your location more seamlessly in the background compared to a PWA.
Always-on background tasks: Some mobile apps can perform actions in the background even when you're not actively using them. For instance, a music streaming app might continue playing music uninterrupted even if you switch to another app. PWAs with service workers can do some background tasks, but they might be more limited or paused to conserve battery.
App Store discovery and installation: Finding and installing mobile apps is usually a smoother process. You can browse app stores with categories and recommendations, and installation typically involves a single click. PWAs rely on users finding the website and then adding them to the home screen, which can be less intuitive.
[...] For many web browsing tasks or simpler functions, a PWA can offer a very similar experience to a mobile app.")
