Should the snap-store be using >300Mb of memory?

The snap-store process is intermittently using hundreds of megabytes of RAM.

Is this normal? Is there a solution?

You can safely uninstall the Snap Store app with sudo snap remove snap-store && sudo apt install gnome-software, and if you do you will still be able to install snap apps from the terminal with sudo snap install package-name and also to manage installed snap apps from the terminal.

There is a temporary workaround. App Outlet is another software center app that has the functionality of searching for snap packages, but if you install it locally in your home directory without root permissions (it is an appimage app) then you have to install snap packages from the terminal. If App Outlet is locally installed (What is an “AppImage”? How do I install it?) the RAM it used should be freed up when it is closed.

I don't think Snap Store's excessive RAM usage is anomalous because other Ubuntu users have also reported the same problem. I suggest that you try App Outlet without uninstalling Snap Store. If App Outlet works as a replacement for Snap Store then you can uninstall Snap Store and install the Software app with sudo apt install gnome-software instead.

I have both Snap Store and the Software app installed in 20.04 and the RAM used by both apps is freed up when they are closed. I'm worried that your Software app will use excessive memory too, the same as the Snap Store does, but if it may solve half of the problem if it doesn't use excessive memory, and you can use App Outlet alongside the Software app as a replacement for Snap Store.

Yeah its normal.

If you are not using snap-store just remove it using -

sudo snap remove snap-store

Instead you can use gnome-software