As the title suggest.
I really want to search in-store for games I already own.
Why?
Common need you ask?
alright, fine. It's because of games I enjoy but don't have installed, I may want to brows those, and look for any that may be on sale, that I might want to gift others.

I'd like it as part of 'galaxy' and as part of the website itself.

Please?

*writes request*

GOG: "Noted."

*discards request, as per protocol*

I fail to understand.

You want to search the games you already own? You can use the search bar in your library to do that. Or have I missed the point of your question?

You missed the point.

He wants to browse the catalogue based on what he already owns, so he can see what's discounted and then gift those to others.

I don't see the point in that request though, all promotion pages should already show what you own after the games you don't own, so it's relatively easy to see them.

Also it is possible to go to "browse all games", then select those discounted. The ones that are owned and wishlisted appear marked. Changing the layout from grid to list might help.