Do you have an architectural salvage company in your area? That's where I would check first.

A tile restoration specialist may be able to make a small piece with matching paint for your missing bit. They can also repair the cracks.

I’ve had some luck in architectural antique stores but it would be needle in a haystack. I think it will be easier to get someone to patch it and faux paint it to match.

That crack has probably been there since 1929. Please don't fool with it. Any type of replacement won't be original fabric and has too much downside risk. It's charming and I could hardly find it in your picture.

I agree leave it alone or replace and IMO since it is not 1928 tile maybe replacing it will work better with your now decor.