I can find the search option on the web page, but not in the Galaxy client.

If you want to search all stores, click the magnifying glass icon in the top left, next to your avatar.
If you want to search the GOG store only, click "More offers" under the Deals category in the sidebar.
If you want to search your library, click "Owned games" under the Games category in the sidebar, then use the search bar at the top, between the + button and the view switch button.

[Ctrl]+[F] :-)