For command line apps, I use paru for AUR. For desktop apps, if they’re available as a flatpak, I prefer that for the increased security provided by the sandbox. Otherwise I use Arch packages or AUR. I even uninstall GNOME apps (calendar, weather) from pacman, and install their flatpaks.

I use an unholy blend of paru, Flatpak, Docker and AppImage apps (no Snap!) with Topgrade to update it all.

pacman + yay + appman (in cases where appimage is more convenient)

If you need something from AUR, Chaotic AUR builds some of them.

Technically I also use managers for certain languages and environments, so sometimes cargo, pip, luarocks, … whatever.

I did try to use flatpak in the past, but I just found it annoying. If you do not explicitly need it’s capabilities for a certain app it is mostly makes accessing app’s config and data a major annoyance imo.

pacman / yay

I also like pacseek as it provides a simple tui for package search and getting info about packages.

Yay

I only use flatpak for one Python program because it has a lot of runtime dependencies I don’t want to bother with. I generally wouldn’t use flatpak.

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.

Pacman plus the AUR is the move on Arch based distros. The AUR gives you access to basically everything, and paru or yay handles the build chain without pain. Flatpak has its place for apps that ship messy runtime dependencies, but for most things it adds an unnecessary isolation layer. Have you tried paru as your AUR helper yet?