With the wall open already, I’d just redo it honestly. Never gonna have a better shot at it, and 70 year old copper thats already crusty isn’t getting any better. I’d go PEX for the supply runs. No torch, no fire risk near old framing, and crimp tool is like $50-80 and you’ll reuse it forever. Sweating copper in tight spots between joists is a pain to learn on the fly.
Keep the last 6-12 inches in copper where it stubs out to fixtures tho, looks cleaner and gives you something solid. SharkBite or proper transition fitting should work. for the clawfoot, supplies through the floor looks way more right than flex out the wall imo. Your already in there so its actually easier now then later. Also swap the shutoff valves while your at it. Old ones seize up right when you need em.
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.