Flatpaks are a way to get applications on Linux. This works independently from the systems package manager.
We recently decided to not support both Snaps & Flatpaks as we got a lot of apps in Chaotic-AUR already / AUR has it all usually. You can request packages to be added to Chaotic-AUR so you wont waste time compiling from source.
If you absolutely need another source of applications, Flatpak should be the one used - helpful is its Archwiki page.
If fish is used as login shell:
Since fish doesnt use /etc/profile.d Snaps wont work right away (eg. doesnt show up in startmenu). There are 2 possible workarounds:
sudo pacman -S bass-fish
for file in /etc/profile.d/*.sh
bass source $file
The preferred workaround is the first one as it is faster and works natively with the environment variables due to bash starting before fish does.