I think you're making a mistake by offering this for free.
The kind of people who care enough about their web experience to install a new browser are the kind of people who won't mind parting with a few £$€ to do so.
To be profitable, free apps must target the broader market, but this is a relatively niche product. I don't think you'll get enough IAP fast enough to be sustainable.
Because the average user doesn't even know what a web browser is, they just open up "the internet" on their phone. They are not going to change something that they're not even aware of. It's also demonstrably true that the average user doesn't know or care about privacy enough to make this choice anyway. You don't have the resources to change either of these things.
So, disregard the average user. Market this as a paid product which offers a superior web browsing experience for the technology connoisseur and the privacy concious. These people, on average, have a lot more money, are easier to sell this product to, and don't mind paying.
Another reason to just charge money for this is that this provides assurances about your income stream which should mean that you are less likely to consider anti-user practises in order to generate income at some point in future.
Apathy is probably your biggest enemy. Look at the struggles Firefox and Opera went to even with the random browser choice stuff in Windows in Europe, which made no significant difference to their market share.
The kind of people who care enough about their web experience to install a new browser are the kind of people who won't mind parting with a few £$€ to do so.
To be profitable, free apps must target the broader market, but this is a relatively niche product. I don't think you'll get enough IAP fast enough to be sustainable.