This has happened because you granted Google to collect all this in your Account privacy settings. For Web and App activity it explains that it collects data from all apps that use play services.
If an app uses play services or not is a matter of if those are installed. So whether you install an app from whatever source, if the program makes use of play services it will use them if the app finds these on the device.
It doesn't matter if this app has network access or not, play services is convenient to use for app developers, so many chose these instead of implementing something they coded themselves.
You also granted Google to collect all your web searches. That is independent from play services, it happens whenever you use Google Search and when you are logged in with your Google account in that Browser.
You can see that in your picture, there appears a search you just made.
So when you are constantly logged in and granted to collect all activities, this was your personal choice and is unrelated to play services or GrapheneOS.
If you don't want this to happen, don't log into Google in your browser permanently and avoid Google Search.