Your question made me curious. ?I'm far from being a security "expert", so please take the following with a grain of salt.

I found this 2024 PC Mag article on this topic:

Lose the Trackers: The Best Private Browsers for 2025

Although the article's title says "2025", it was last updated in October of last year. ?It mentioned a couple sites that can be used to check this:

Privacy Tests

It has several tabs across the top, for different browser categories (desktop, desktop private modes, iOS, Android, etc). ?Each category only uses a browser's default settings. ?I was amazed by the number and types of trackers.

Cover Your Tracks

Apple's webpage says, "Some companies use this data to try to uniquely identify your device — known as?fingerprinting. To prevent this, whenever you visit a website, Safari presents a simplified version of your system configuration. Your Mac looks more like everyone else’s Mac, which dramatically reduces the ability of trackers to uniquely identify your device." ?So Apple doesn't try to fully hide your system. ?Instead it tries to make it look like a generic Mac. ?Take that into consideration when reviewing "Cover Your Tracks" results.

I had "Cover Your Tracks" test Safari on my iPad (iPadOS 18.4.1) in both regular and Private browsing modes. ?The latter did better than the former. ?This is contrary to articles that I've read, which all said that Private browsing only removes data at the end of the session, and therefore doesn't provide much tracker protection. ?So, if you're concerned about trackers, use Private browsing modes, but I think that will require you to login more often to sites that you frequently visit (cookies automatically deleted).