On Linux you can run native version of Steam, which then uses Wine (actually Proton, which is based on Wine) for running games. So Steam is not wrapped within Wine, but the games are (if needed/enabled)

does it allow you on Linux to download all games with the native client?

yes, and then you run them using Proton, Valve’s tool based on Wine, specially made for doing exactly that.

Steam on Linux has it’s own version of wine(proton) built in.

So you can launch Windows games through the Linux native Steam client.

There is an option in settings to allow trying all games. By default it only allows it for tested and verified games. But it is a simple checkbox then you can download and run any Windows game.