Steam introduced a feature some years ago where you change your start screen in the shop to show only games that support a specific OS (Linux, Mac, Windows).

I would love to see such a feature for GOG, too.
As I'm only buying Linux native games, I would love to also just being informed about such games.

There's a filter on the store page. It's below tags. Probably does what you're looking for.

However, if you're being really restrictive in your definition of "Linux native games" (i.e. games that are made for Linux and aren't run through Wine), that's may be too niche for GoG to care about as they are more focussed on "will it work in that OS".

One of the Linux users on this forum (they usually pop up in most threads where someone mentions anything OS, driver or hardware related - almost like they've got summoning bells) might be able to assist further.

To be fair there are very few games on GOG that come with WINE wrappers. And unless I missed some all have been added to the store a long time ago, so I suspect there is nobody still working for GOG with the knowledge to setup that kind of wrapper.

Most of the games sold as native are:
- running with ScummVM
- running with DOSBox
- using a real Linux native engine (this would be most of them, by a very wide margin)

--- My summoning bells rang ;)