Indoor/Outdoor Carpet is about your only option.

That’s what was in there before but it developed a white mildew/mold around the edges

As would anything installed for this application There is nothing that that would not happen with again.

I was curious about these interlocking deck tiles, what do you think ?

https://www.wayfair.com/home-improvement/pdp/courtyard-118-x-118-stone-interlocking-deck-tiles-in-gray-lbng1024.html

The moisture will be trapped and cause mold on the concrete.

What about adding some sort of treatment to the floor rather than flooring?

Here is a before and after of poorly installed concrete that was treated with multiple layers of 2 part polymers in different colors (like sponge painting), with a clear sealer with glitter and a dark brown border

Sure as long as you follow all the same prep steps as the driveway if you expect it to last more than a few weeks.

I was thinking you should have one of those companies that spray garage floor coatings out to look - pick a color/texture that might resemble terrazzo and then just use an area rug