Could a radar distinguish between a Tomahawk and SLCM-N? AGM-86 and JASSM-ER, or LRSO and JASSM-XR for that matter?
No. You'd wait until initial battle damage reports to decide if you want to nuke the other guys and by how much. Everyone does this.
Like maybe a sub-launched CPS vs a Trident D5 on a depressed trajectory, or even a D5 LE on a depressed trajectory with PGRVs at some future point.
The only purpose of such a thing would be to attack nuclear weapons while keeping nukes in reserve to threaten population attacks.
The entire point of Prompt Global Strike and its spawn (CPS etc.) was to destroy North Korean/Iraqi/whoever's ballistic missile TELs quickly because it was an outgrowth of WARBREAKER. We know how to find the TELs (air/spaceborne GMTI), we have the means to store their locations (WARBREAKER), and now we need to kill them (PGS).
It's all very point, click, delete. I'm sure it would be handy to have for beating "A2/AD" or something maybe.
Somewhere in the Combined Arms School library at Fort Leavenworth there's a VHS tape that talks about this.
Even in a limited strategic nuclear exchange I suspect that they would be priority targets.
It would be easier to launch killer cubesats to poke holes in a constellation, than set a precedent that denies access to space, I'd think.
That is certainly an issue with SLCM-N, especially off of subs. The air-launched missiles are less of an issue since it is unlikely that they would be used for a decapitation strike and bombers are typically used for signalling, which means you want the other side to know that nukes are on board.
It's a war between two nuclear armed superpowers. Nukes are on the board from the first minute. It may even open with nukes, against Okinawa and Yokosuka, to neutralize the U.S. forward deployed CSG and Marine aviation units. No one really knows.
The only thing that is reasonable to assume is that leadership classes in either U.S. or PRC would rather take a small L than commit suicide.
Escalating a limited tactical nuclear war to a strategic exchange is silly and in this era of high connectedness and telecommunications, the bilateral back and forth through neutral intermediates (the European Union? France? Germany?) should be pretty good compared to 1985 or whatever, when the Soviets would be slamming every Swiss bank with a few kilotons to liberate captive gold from its slavery. Decapitation strikes are useful against undeveloped despotisms, and their tinpot dictators, but not against nuclear armed nations.
Russia doesn't seem terribly interested in hitting NATO shipments in Poland directly, at least until they transit into the combat theater (Ukraine), so it's hard to imagine why either the U.S. or PRC would want to attack each other's mainlands over Taiwan or sandbar bases. The two belligerents are even fighting a proxy war in Africa, so non-nuclear third nations are also fair game, and the United States has no real designs on striking Russian leadership or whatever.
Anyway, nukes will be on the board instantly if only because the sole playbook on "how to crack open a U.S. carrier battlegroup at sea" involves using at least a dozen or two nuclear missiles. Milan Vego has a book on the subject specifically.