There has been a few instances of trying to get an app off of Pop!_Shop only to be met with an extremely out of date app.
I’m no expert, still very new, and I have no idea how the Pop!_Shop functions, but what is the process of getting apps updated? Is there something users can do, or do we just have to wait for the updated version to hit the shop?
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.