Terracotta look tile. 18" x 18" size.

Porcelain Tile ONLY. Matching brick and terra cotta and orange wood floor is tricky. In theory it can be done with something very multi tonal. https://www.marazziusa.com/products/cotto-look/cotto-revival/rust

But the safe choice is to do something in more of a slate gray look.

https://www.marazziusa.com/products/cotto-look/cotto-revival/baltic

https://www.daltile.com/products/stone-look/scripter/rebel

https://www.daltile.com/products/stone-look/haddonstone/velvet

Or an authentic slate look, with variation and texture that's the best mimic around.

https://www.daltile.com/products/stone-look/delegate/black

Thoughts on luxury vinyl plank out there?

LVP can fade in sunlight.

Slate or slate look tile

A brick-look tile or brick-look clay/concrete paver in a herringbone pattern.

Here is an example. Per the owner/designer the brick floor is from Inglenook Tile: www.inglenooktile.com. They are actually thin brick tiles that can be installed just like any other tile.

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LVP is vinyl and it really moves a lot, even more so in a sunroom. Really needs to be in a climate controlled area.

Paint the floor the same color as your existing wood plank floor. It will connect the two rooms nicely. Find a large rug to add coziness. Done. Save the money for other projects.

How about an indoor/outdoor carpet? You don't mention the size of the space, so go with off the bolt, cut to fit? There are so many patterns and different shades. Maybe match the wood floor in your living room?

https://www.sisalrugs.com/all-weather-indoor-outdoor-rug-collection?color=costa-rica-sisal

You could use bricks as suggested above - you could paint the brick that's currently on the bottom of the walls + use brick or porcelain tiles that look like brick:

This is a porcelain tile that looks a lot like actual brick:

This is also porcelain tile that looks like brick:

I don't think that porcelain slate is a good imitation. As long as you purchase good quality natural slate, you won't have any issues (upkeep is easy/it's very durable/it's not slippery when wet). Charcoal/gray/blackish slate from Brazil is a good choice. It comes in many sizes/shapes:

You can use a color enhancing sealer which will make the slate more uniform + darker if you want:

It looks nice with red brick:

Riad tile just started offering slate in a few colors (from Brazil):

There are other colors - but you need to find out what the place of origin is in order to avoid slate from China that is not very durable and tends to flake/peel quite a bit.

"Blue rug not staying"-but is another planned? If not just paint how about sheet linoleum. Tile is a very difficult material to change. If you go slate/tile me sure it's not a statement--it will be there FOREVER and you will tire of it if it's bold.

How will you use the room? Design your seating area(s) first. If it gets damp or wet out there, be very careful that your choice of floors will not be slippery when wet. I like gray with brick, something with a simple pattern due to the busy look of the brick.

You could do the whole room in Flor tiles as it will be soft and cozy but also easy to maintain. https://www.flor.com/
Order some samples and wait until they have their 30% off sale with free shipping. Much more cost effective than tiling the whole room and also adding a rug.