The closest experience I have is a GrapheneOS device where, after installing the Play Store, it ~daily tries to background install some VR app, no idea what that's about (purple hexagon logo, don't remember the name). I don't want this VR game on a work device. Installation fails because it requires manual confirmation (the store doesn't have background install permissions, which I think confuses the heck out of this google thing which is used to being a backdoor with superpowers) but the home screen keeps doing this animation to show another where this app is now loading, and fails some time later. For some reason it stopped prompting me with every attempt, not sure how I made it do that, but it switching home screens whenever I pick up the device is also annoying.
Background installs are totally a thing on the Play Store.
From my limited Googling at the time it seems you will only be prompted to install it if you already have an app installed that depends on it for certain functionality. Do you have any apps that might want to use the camera with AR-like effects?
Personally, I also stubbornly pressed "decline" on all the requests to install it. However, I gave in once I realised that:
1. I was probably the one that caused the install prompt (by installing Snapchat)
2. The shadiness of the app would likely not be worse than the other similar Google services I had already voluntarily installed
3. It would likely not be active except for when I'm using Snapchat
Now I haven't thought about that hassle in weeks.
Yes, the play store already does this.
As monetization becomes a bigger concern for a new app/service that was successful, I would tend to think that after a few cycles of getting better apps in general will get worse by increasing the amount of advertisements, requests for subscribing to something and dark pattern usage.
There's also the case of apps getting worse due to some company wanting to deprecate some feature in favor of another that is actually worse (some chat application that changed the way of doing video calls to take three clicks with loading times instead of one click ; some VPN app which changed the method of logging in so it takes one minute instead of one second)