Not for long. The search page by default shows one non-contextual app above their ranked list of apps you might like.
> App Tracking Transparency allows you to choose whether an app can track your activity across other companies’ apps and websites for the purposes of advertising or sharing with data brokers.
https://support.apple.com/en-us/HT212025
Apple does not track you across other companies' apps and websites so I don't see how this is related. Facebook can still do personalized ads even if you click on "ask app not to track".