On Ubuntu applications installed by the system are located at /usr/bin.
Ubuntu has two default package managers: apt and snap. And they're both located inside /usr/bin:
$ which apt
/usr/bin/apt
$ which snap
/usr/bin/snap
This is the default and completely expected for most GNU/Linux distributions.
Installing other package managers
Both dnf and pacman are included in the Ubuntu universe repository - meaning that volunteers have compiled and packaged it for use directly in Ubuntu.
For starters, make sure to enable the Universe repository.
To install another package manager in the first place, you simply install it with apt like any other application. And afterwards, the new package manager is available to you.
DNF
The dnf package manager is available since Ubuntu 22.04 (Jammy). It can be installed with:
sudo apt install dnf
You can check its location afterwards:
$ which dnf
/usr/bin/dnf
Pacman
The pacman package manager is available since Ubuntu 22.10 (Kinetic). It can be installed with:
sudo apt install pacman-package-manager
You can check its location afterwards:
$ which pacman
/usr/bin/pacman