Did you try the audio troubleshooting from the Pop! Documentation?

https://support.system76.com/articles/audio/

What I described is largely about self managing a few select packages without a package manager.

It is good to think about if you really need the newest version of an app. Do you want a newer version just because it is newer, or does the version in the official repos actually not provide features you need.

If you want the Pop! Shop, which is basically a gui for apt and flatpak, to manage your packages, you will need to add some thrid party source to your package sources. For Ubuntu based distros the most common method for adding a third-party source for software is the PPA. Read up on PPA so you understand the potential drawbacks. There are other mechanisms available, and generally described if provided by the developer.

The packages available in Pop_OS by default are what Ubuntu and Pop_OS maintain. The vast majority of available packages on Pop_OS are what Ubuntu released with LTS 22.04. They do not provide feature updates to packages, only security updates. There will be no package feature updates until Pop_OS rebases off a new version of Ubuntu. Pop_OS maintains a handful of packages themselves, like Firefox. We as users are not involved in package management for Ubuntu or Pop_OS.

If you are interested in community maintained packages for Ubuntu based distros, Pacstall might be interesting to you. I don’t think there is a way to integrate Pacstall with the Pop Shop.

There are alternative ways to install apps outside the official repos. The best options depend on the applications and your comfort level/knowledge.

I tend to get precompiled apps directly as tarballs from the developers and place a symlink into $PATH, like $HOME/.local/bin. Depending on the app I will also make a .desktop file in $HOME/.local/share/applications.

AppImages from developers can be aliased in $HOME/.bashrc and .desktop files added to $HOME/.local/share/applications. Make sure libfuse2 is installed. AppImageLauncher is a handy way of integrating AppImages.

If a developer distributes a .deb themselves, it will very likely work just fine on Pop. It seems that .deb are generated with the assumption an Ubuntu LTS or previous Debian release. If they are targeting only the newest version of Ubuntu or Debian, they tend to state it.

I don’t use alternative package managers like Homebrew and Nix, but they are an option as well.

Then there is always compiling from source, but it is rarely necessary, unless you want the bleeding edge of an apps development.