Before
integrations were abandoned and stopped working, GOG Galaxy was intended to be an all-in-one launcher that gathers your games from various platforms in one place. This, and perhaps GOG's partnership with the Epic Games Store, accounts for the search function bizarrely not putting GOG's own store front row and center.
All you need to do is expand the
GOG Store section on the sidebar on the left, then click the
All Games menu item there. This loads that section of the website, where you have a search bar in the top right and advanced filters on the left.
Confusingly, the Search option under the GOG Galaxy section is less useful for finding things in the store:
1. Expand the GOG Galaxy section in the sidebar on the left.
2. Click the Search menu item and enter the title of the game you're interested in.
3. If you click a game in the search results, this acts the same as the Show Game button. You're taken to a page with details about the game. If it's available on GOG, this is made clear on the right side, where you can click the View in Store button.
While that same button is also available in the aforementioned search results, you must use the arrow keys if you want to select something other than the first item there. It's awkward.
If you have suggestions for improvements, click the cogwheel in the top right, then choose Share Feedback.