Disclaimer: happy iOS and Android user -- I like both platforms and think both have strengths and weaknesses. Mostly a Linux user on desktop.
> Do they know that google pays Apple... to be default search
This statement comes off a bit ironic in the fact that you are pointing out a deal that Apple has with Google -- the current steward over Android -- as a reason that Apple isn't a bastion for privacy. This irony highlights the fact that one is often worse-off from a privacy perspective in using Android -- the main competitor to iOS -- because it is built with Google as a first party.
I absolutely agree that there is an exaggeration of privacy with Apple. But in most cases, iOS does actually do privacy better than Android. Private Relay, App Tracking Transparency and Google not being a first-party in the development in the Operating System are things that come to mind. Additionally, according to a research paper done in 2021, Google collects around 20x more data (around 1+ TB every 12 hours) on Android compared to iOS (around 6 GB)[0]. Even if the methodology behind the paper wasn't perfect (which Google claims) I don't think anyone would be surprised that Google collects more information than Apple.
My opinion is that the sweet spot for privacy on a mobile device is to buy a Pixel (for the great hardware security benefits) and go with a custom, de-Googled ROM like CalyxOS and try to use F-Droid for all your apps. For those who are even more hardcore, GrapheneOS is awesome.
In my opinion, stock Android is far worse for privacy than iOS simply because of Google's first-party influence. And then if you go with a vendor like Samsung you not only have Google as a first party on your mobile device but also Samsung.
The only option left if you want more privacy on mobile than an iPhone is to either flash a de-Googled ROM, like I said earlier, or to go with some sort of Linux distribution on mobile -- both of those alternatives come with huge downsides.
(Sorry for the rant, I always find this topic interesting)
[0] https://www.scss.tcd.ie/doug.leith/apple_google.pdf