What part of the country do you live in?

You could take the tile to Benjamin Moore and let them use a color meter/detector/scanner to read the color of the spot on the tile you want to match and either custom-blend something for you or point you to the nearest match. Always get a test pint and paint it on a large board or sheet of something or the wall itself before purchasing the gallons. The sheen can make a big difference in appearance of the color. I recently did a couple of rooms in Benjamin Moore's Aura paint from the Affinity collection in satin sheen, and it was initially a little more reflective than I had wanted, but I love it now, and it's very easy to clean if needed. Aura is the most water-resistant of the paints and good for kitchen areas.

I don't, but if you click on the link that says "More Info" below the photo, you'll see which pro posted it on Houzz. You could then message them to ask whether they still have the color/brand on file. I would bet money that the Benjamin Moore store could find you a sage green in their Historic Color palette that is very similar.

We were able to match the mortar color pretty well and ended up with Coventry Gray. It's not too warm, and not too "blue" or "purple" which was how some of our other test colors ended up. It's also lighter so it doesn't fight with the awkward brick and roof colors, like @la_la Girl mentioned! This visualizer pic seems pretty awful lol, in real life it's a nice match to all the elements. Thank you all for your help!