I think that's true, but that the most likely use of nuclear weapons is when/if Ukraine tries to retake Crimea.I think you are missing the point, its a "here is a taste of what you could get, now lets sit down and talk about how much of your country I will take and the demilitarisation of the rest". Btw Little Boy was around 13kt yield - very much in the tactical class by today's standards.
I'm not convinced that Putin has tried everything to win the war. I think he may well consider a final destructive blow, before withdrawing. His goal now appears to be to cause so much destruction that Ukraine will be screwed for decades.
It's hard to justify nuking a country you're trying to liberate from Nazis, but nuking the invading NATO horde as it tries to cross into Crimea? That is an easy sell, plus it would actually work.
Putin views Crimea as a done deal, it's Russian territory now for him. Losing that would be a much greater blow than losing the rest of the Donbas from 2014.