meiklmue Have you ever rebooted your device while an app is installing/updating? I remember one time long ago that Google Play Store caused a noticeable slowdown of my device, so I tried to force stop it. That didn't help, so I rebooted my device. I think I confirmed that Google Play is entirely stopped (maybe I disabled it as a temporary measure?) yet the slowdown was still happening after rebooting. When the slowdown ended, I opened Google Play Store and discovered that a few apps that were previously stuck updating (or something like that) just now finished updating. (The slowdown is caused by GrapheneOS fully compiling the app to machine code when you install it. This isn't the case with modern Android anymore which installs apps instantly and compiles them later/on the fly.) If you open an APK, especially large ones where it's more noticeable, there is a "Staging" part before it asks you if you want to install/update the app. This part is where it copies the APK to its own private temporary storage, I believe it does it so the app that is being checked against security restrictions during installation with the icon and name displayed to you wouldn't be able to be changed between you seeing the name/icon and these checks occuring, to you actually approving the installation. In short, when an app is installed or updated, its APK is copied into a private temporary location, and once the installation starts, the OS keeps installing the app independent of the app that initiated the installation. If you completely stop a user profile, or even reboot your device and not unlock it, any updates that were downloading but not yet started would be stopped, but any updates and installations already started should still continue to completion in the background, even when no apps are running.
Maybe relevant: I also found this nice infographic on Android's website (describes Android 10+):
https://source.android.com/static/docs/core/permissions/images/package-install.png
https://source.android.com/docs/core/permissions#package-install-and-permission