If you're worried about cross-site tracking, specifically, take a look at Cromite, the browser.

Going beyond Adblock, it's stuffed with “anti fingerprinting” measures like randomizing your resolution and time, your hardware and drivers, JS execution speed, anything that could be used to try and uniquely identify your PC. It’s SOTA at that as far as I know.

Sounds like exactly what you need as a “backup browser”, as its designed to anti-fingerprint with JS enabled, neutering certain JS feature's by default.

…But that’s just one form of privacy. If you are worried about any entity logging your visited IPs, you use a Tor browser or something like Mullad.

I’ve been a two browser person for over 20 years. It might not be for everyone, but I do all my browser activity that has an information risk (banking certain types of ordering, health access, etc.) on one browser with a specific security profile to protect those sessions, and all my other browsing on a FireFox variant locked down with NoScript, Privacy Badger, uBlock Origin, etc.

This means that I always reach for the properly configured tool when doing something online, and attempts at phishing have one more hurdle to clear. Default browser points to a fully locked down profile, so any stray clicks will do minimal damage. Sites I know are sandboxed and not allowed to access anything on the rest of the Internet.

This configuration isn’t for everyone, but I’ve been on the Internet for over 35 years and still seem to have a reasonable amount of privacy and security.

For sites you visit occasionally, it's better to enable tab isolation (use the containers feature) and then enable JS only for that domain (note the difference between allowing JS from that domain in any tab, vs only allowing that tab with that domain to use JS, you should do the latter)

https://addons.mozilla.org/en-US/firefox/addon/multi-account-containers/

If you're switching to a different browser you may as well use the same browser but a second clean profile and use private tabs so it doesn't retain history. Using private tabs in your main browser profile does also help but isn't perfect because there's still some metadata leaks occasionally.

Using a different browser could ironically make you easier to track - how unique you are is the main signal used to track you (user agent, OS, language, etc), and going for an even more rare config will help their tracking even if you delete session cookies. Especially if they have a tracker across multiple domains you visit from different browsers from the same IP, with similar device fingerprinting results across browsers. That's a strong signal those sessions are linked. You want to NOT stand out to maintain your privacy.

I usually allow websites to run their first-party scripts on their own domain without much of a second thought (using NoScript on Firefox). But my threat model is likely more lax than yours.

I wish more people used Anubis instead of Cloudflare, I am a little concerned with how often I have to allow the latter to run their script to even access a website...

Why not go for an even more hardened browser like Mullvad or Tor if you are so worried about privacy while browsing regular stuff?
LibreWolf is my primary browser as well, so it's for daily, non-sensitive, use, so I have JS enabled because, well, non-sensitive stuff, and it's just a main-online identity, but I do use other browsers for other stuff, and change my VPN when I'm going for other "identity" too.

I strongly recommend the uMatrix-Addon for FF/LibreWolf. It gives you maximum control about all the requests your browser does.

Tracking from WHOM and thus WHY should be the question.

It's different to be tracked for profit, e.g. Google or Meta, versus for political or corporate espionage purposes.

The former is basically volunteering information through bad practices. Those companies do NOT care about "you" as an individual. In fact they arguably do not even know who you are. Avoiding their services is basically enough. It might be inconvenient but it's easy : just do not.

The later is a totally different beast. If somehow the FSB, because you criticized Putin, or NSO Group, for something similar or because you have engineer something strategic to a business competitor who is a client of theirs, then you will be specifically targeted. This is an entirely different situation and IMHO radically more demanding. You basically don't have to just care about privacy good practices, which is enough for the former, but rather know the state of the art of security.

So... assuming you "just" worry about surveillance capitalism and hopefully live in a jurisdiction benefiting from the Brussels effect with e.g GDPR related laws, either way is fine.