The M4 was designed to be a punchy race bike. I had Kleins of the same generation and boy are they stiff at the back; Cannondales the same. It’s a tangible stiffness - instant acceleration and absolute precision tracking down something rooty and flinty. By contrast, steel 853 Cotics, double-tube rear Bontragers, etc all nice and compliant in the rear end.
But there can be more than one reason for back pain. Yes, shocks from a stiff end, but also reach and position. Being overstretched is a BAD THING. Running really long gear and pushing too hard can mess up your back something rotten.
Mitigation:
Measuring reach and position and matching your M4 to the position on your steel bike. If you do not have an in-line post on the M4 do try pushing the saddle forward on the rails so that you are more forward over the BB.
Bigger tyres running at a lower pressure - but watch over-large tyres on narrow rims.
titanium seat post of narrow section running into a seattube shim.
All worth thinking of. But the biggest pain I had in my back was on a steel Marin, light speed down a hill and then onto baked washboard ruts caused by cattle marching through a narrow section. Instant ouch as the bike bucked four or five times really viciously. Yes, modern full sus can be good for a sore body.