Maybe I've watched Dr. Strangelove too many times, but everyone knows that flinging all of your nukes at someone kills you too (the "Doomsday Device"), so what I'd expect to see in WWIII is two things: 1) the clash of a ton of new technologies where we have really no idea what beats what, and 2) strategic, low-yield nukes used against blue-water navies and ports.

But now both USA and Russia have far less nukes (and with smaller yields) so now the effect of a full USA-Russia nuclear exchange would be much smaller - but we are not even talking about that; we're talking about China, which has something like 250 warheads (contrast to ~45000 warheads that USSR used to have, it's more than a hundredfold difference) - it's a sizeable deterrent, but it's not mutually assured destruction. MAD was the doctrine between USA and USSR or Russia; MAD does not apply for any other nuclear powers - China, France, UK, India, etc. A nuclear exchange with them is "only" mass murder, but nowhere close to an extinction level event.

There's proxy wars like we saw in Korea and Vietnam during the Cold War. There's cyber attacks and other acts of sabotage carefully cloaked in plausible deniability (for example the 1982 Siberian pipeline explosion, Stuxnet, the attacks on Sony attributed to North Korea). There's limited wars where there's actual open fighting, but neither side is prepared to escalate further (think of the Falklands War, the War of Attrition between Israel and Egypt, or any number of peacekeeping actions by the UN or NATO).

Total war between major powers has gone away, but war is here to stay.