If the US supplies JASSM-ER they will be in violation of the MTCR.
You can easily interchange warhead with fuel in a cruise missile. 450kg warhead is already pushing it close to the limits, and 757 mi range is in violation. They already stepped on that line by providing such missiles to Finland and Poland, and this is likely to cause a future direct conflict with Russia as it is. Their claim, as usual, is that they can supply whatever they want to NATO countries. What will likely happen is Russia will withdraw from the MTCR and start supplying long range cruise missiles including related technologies for their licensed production to Iran, North Korea, Algeria, Venezuela, Cuba, and whomever. The Mediterranean, the Persian Gulf, and the northern Pacific will be closed down to US carrier battlegroups whenever those countries wish, and probably huge chunks of Africa as well.
So they should pick their poison properly. It seems the US haven't gotten the memo with the Houti blockade yet.
The US leadership is particularly stupid in that they seem to think they invented the cruise missile or have some sort of technological lead in that technology. The truth is both the US and the Soviets made copies of the German V-1 buzz bomb from WW2 and then kept upgrading them. Expect that the Soviets and Russia spent way more money on this for decades, because they have to fight US carrier battle groups.