Quit the application -- in this case, snap-store (a.k.a. Ubuntu Software). Since snap-store auto-starts upon login, you might not recall that you have it open...but you do.
- Closing the window is not enough to terminate the application.
- One way: On the command line, run snap-store --quit
- Another way: Open Ubuntu Software, look at the top bar, find "Ubuntu Software" on the left side of the top bar. Click it, and select "Quit".

Run sudo snap refresh. Let the command complete.
- If, instead of a refresh, you still get a pop-up that the application needs to be refreshed, then run sudo snap refresh <application-name>.
  The output of that command will return the PID causing the block.
  Use kill <pid> to remove the block.
  
  Run sudo snap refresh again. This time it should work.

It's now safe to re-launch your application.
- If you were not using the application before, or you don't know how to launch the application, then you can safely ignore this step.

Second, let's talk about WHY it's happening:

Snapd detects when a new version is available. If the application is currently running, snapd will inhibit updating that application for up to 14 days.

With most applications, this works fine. You Quit out of an application, a few hours later snapd updates the application (it checks several times each day). and the next time you open the application you don't even notice that it's been updated. Great!

But some applications are open for a long time that runs up against that 14-day window. Like web browsers on laptops that get closed/suspended instead of quit/restarted. Unfortunately, when the 14-day window expires, snapd will kill the application in order to implement the upgrade. To the user, this looks like Firefox crashed unexpectedly, losing whatever they were doing.

Snapd MUST refresh snaps. That's a legacy of the original design; snaps were originally designed for phones and IOT devices that MUST work reliably and MUST update reliably without user input. You can disable it if you know how...but it's a bad idea for most users -- disabling updates means no security patches and insecure applications.

Third, let's talk about why you are suddenly getting these notifications NOW.

The Snap developers were dissatisfied with those two choices (kill the application to force the upgrade -or- disable upgrades entirely), so they created a better path: Remind the user to Quit the application when convenient. That is the notification you are seeing. It's new (turned on by default) in Ubuntu 22.04.

If you ignore it, then when the countdown reaches zero snapd will terminate the application and refresh that snap automatically.

Finally, there's one obvious question remaining: Why isn't this automatic? or perhaps Why doesn't snapd download the update before nagging you?

Well, that's a work in progress. The snapd developers welcome code contributions to help make that happen safely. Snapd is Open Source.

Most folks who encounter this issue simply have not used long-lived Snap-packaged desktop applications before. It's a known problem, and various developers are working on it. You are welcome to help them.