That grey top layer is almost def self leveler the flippers poured over the original mortar bed, and thats whats cracked. The aggregate stuff under it is your real 1958 slab. Self leveler cracks like that all the time when its poured too thick or without primer, which flippers never do right. Tap around with a hammer and listen for hollow spots. If the original slab sounds solid, I’d just chip off the leveler down to the real mortar bed. Annoying but way less work then ripping it all out.

From there honestly I’d skip pouring new leveler and just go Ditra straight over the slab with thinset. Handles minor imperfections and gives you the decoupling layer the flippers skipped, which is probly why the tile failed to begin with. Wouldn’t tear the whole slab out unless you find its really busted underneath. Huge job and you’ll open a can of worms with the joists.