I’m going to suggest carpet: specifically Stanton Anywhere. I love this product. Available in many colors and designs, I think it would abut your hardwood beautifully, and no need to remove existing tile.

It is what it says: solution dyed, it goes anywhere. I have it around my pool, over concrete, and it suffers 4 seasons of New England weather for the past 5 years. My hubby has power washed It once.

Interior use, it looks like sisal/jute. Take a look before you say “no”.

https://www.stantoncarpet.com/CGI-BIN/LANSAWEB?wam=WPRDLST&webrtn=productList&ml=LANSA:XHTML&part=CEP&lang=ENG

Cute pooch.

Would not carpet that sun room. Would either try to match flooring of adjacent room (looks new; flooring still available?) or go with a brick look tile -- something similar to your fireplace if your home has one.

My fireplace has a slate looking tile. I like that idea, but it is dark gray and I was looking for a lighter look. But I like that direction you suggest.

Judy, that is a great idea--the Anywhere collection looks fantastic!