Visit your local independent tile stores, not big box. They will have a wide variety of porcelain tiles at all price points. Visit several stores, because some of them will have exclusive rights to carry certain lines.

The Delegate in the black has the same exact appearance and slightly irregular texture as my sister's 60 year old slate foyer.

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

Enlite has a good limestone looking appearance, and comes in large sizes.

https://www.daltile.com/products/Stone-Look/Enlite

I know that your question is for a slate looking porcelain tile. I just wanted to ket you know that as long as you purchase the correct type of genuine slate tile, it is easy to care for/maintain. I have black (charcoal) gauged and honed slate tile from Brazil. It does not have clefting/splitting issues - and can even be used outdoors. My installer used a impregnating matte sealer on it. However, prior to being sealed, my older dog threw up on it - wasn’t noticed for a few days - and it cleaned up easily with no resulting marks/damage.

Also, slate is not slippery - even though people will tell you otherwise. I’ve lived with it in a bathroom + mudroom/laundry room. It is not slippery.

I am using MSI Montauk Black slate in my lake house because it is easy to maintain (and not slippery when wet). It is also gauged but has a little more surface texture on some of the tiles. You can sort through boxes in order to get the look you want. I think that natural slate looks much nicer than faux slate, As long as you don’t purchase slate mined from China - and stick with slate that originates from Brazil, your floors won’t require a lot of maintenance.

FYI - while renting a condo in Aspen, CO, an entire bottle of olive oil was dropped and the entire contents spilled onto a slate floor. Some of the oil soaked into the tile - however, it wasn’t difficult to remove it from the tile and we received a full refund of our deposit.

The type of slate matters - some slate is porous and will cleft easily - others won’t. Charcoal slate from Brazil is not expensive. The MSI slate was under $4 sf for 12x24 size + around $4.60 sf for the 4x12 to be used in two of the bathrooms at the lake. I’ve tested it - (including spilling many things on it + leaving pieces outside in freezing rain + temps below 10 degrees). Zero issues re staining or splitting.