Running Ubuntu 20.10.
My software center hangs whenever I search for a software using the magnifying glass.
I have the flatpak extension enabled, it that's relevant.
For me, disabling "App Search" for not needed apps fixed the hanging.
To do that open the Gnome Settings -> Search -> Disable apps one by one until you find the one that causes the hanging.
killall snap-store
on the command line (then re-start) always fixes it for me. I usually do that anyway after closing the store as for whatever reason the snap-store process stays running in the background and uses a LOT of memory.