I use yay, as it comes by default with EndeavourOS. It’s basically an AUR helper that uses pacman and works quite the same.

Flatpak is a different package manager and has nothing to do with your system packages. They are not exclusive, I use both. So what you basically asking isn’t which package manager people use, but rather which package format.

If you have to ask this, then its probably good idea to stick to systemd. I don’t see any reason to change, other than to protest. In the process doing so you will probably encounter issues. People switch away from systemd for various reasons, but not for performance. In example they don’t like who develops and controls systemd. And they don’t like that it does more than just initializing the system, as bunch of other tasks are bundled into it. If all of that does not bother you, stay with systemd in my opinion.

And if you really want to switch to systemd, then I recommend to use a dedicated operating system (a distro) with that in mind. Don’t forget, that systemd has many features and services, that its expected as a standard. You do not just change an init system, but replace all other components too.