No comment on flooring but for your mats. Get a WaterHog mat that runs the length of the room. Mine doesn't keep all the dirt out but it really helps.

Can you use the same slate?

I did matte black hex tiles with grey grout

Slate is perfect in a mudroom, and because the mudroom area is open to the room with the slate, using the same tile would be best. If you don't have anymore of it and can't get more, use a varigated hex that has the slate color in it. It looks like it's too late for this comment, but I wouldn't have used white grout with the slate. Dark gray would have been so much easier to keep looking clean.

I have waterhog mats at all of my exterior doors, so I agree with aziline, they are great.

Why isn’t the same slate the first choice?

It is a very old house and this is the original slate so we would have to colour match it. I regret that there is white grout but there you have it! The mats in that room are just temporary over concrete.

you can choose any tile that interests you.

Looks like you will still have a threshold, so it won't be a seamless transition anyway.

Do something fun, chances are, it will become a drop zone with clutter anyway.

The house might be old but the slate isn’t. Looks like Vermont slate 18” square? Match it, get all grout darkened. I just had a client us Mr grout and the results were terrific. They had similar floors to yours but the tile was 4/12 so it was super busy, they now have charcoal grout and it’s so much calmer.

I would bet you can find that same slate not a rare thing at all. Then do the same floor make your life esy if you want youcould do a bit darker grout . I also ,like Waterhog mats