Hi again, @Jim4444 
As far as I can tell, that bug of "App Center" (which is now the same thing as snap-store) not showing Debian packages, in Ubuntu MATE 24.04 LTS ("Noble Numbat"), even when we change the selected option in the "Filter by " dropdown list from "Snap packages " to "Debian packages", is fixed in the current version of "snap-store" which is 0+git.ec3fa65 (1147)
So, my suggestion is for you to please do the following:
1. - Close the "App Center".
2. - Open a "MATE Terminal" window and, in that "MATE Terminal" window:
2.1. - Run the following command to guarantee that there are no more processes running from "App Center":
killall snap-store
2.2 - Run the following command to see what version of snap-store
is currently installed:
snap info snap-store | grep 'installed:'
2.3. - Run the following command to update snap-store
to the latest version:
sudo snap refresh snap-store
2.4 - After that previous command execution completes, run the following command to see what version of snap-store
got installed after that update:
snap info snap-store | grep 'installed:'
3. - Open the "App Center" by going to the "Ubuntu MATE" menu -> "Administration" -> "App Center".
4. - In the "App Center" window that opens, do a search for gparted in the search bar located at the top. It will probably still show "No results found for "gparted" " as shown in the following screenshot:

5. - In that same window, change the selected option in the "Filter by" dropdown list from "Snap packages " to "Debian packages" as shown in the following screenshot:

... THEN, now you should get the "GParted Partition Editor" in the search results area, as shown in the following screenshot:

I hope this helps
Please reply again to this topic to tell us if this solved your problem.