The problem with this is that Russia is not trustworthy at all. The other problem is, that as soon as it officially annexes the Donbass and the Cherson oblast (as they already prepared), they would claim the war is happening on Russian soil. That allows them to deploy conscripts without calling it a war and it also kinda allows them to use nukes and still claim they are only defending Russia proper and that this was an existential threat to Russias existence.
So, I'm pretty sure conscripts are already being used in Ukraine. The Russian government has claimed they were deployed there accidentally, which frankly raises more questions than it answers, but I doubt they've been pulled out. What the government seems to have been desperate to avoid is conscripts being in intense fighting and suffering large numbers of casualties, because that would become a domestic political nightmare. I don't think that situation is going to change regardless of what happens.
Russia's nuclear doctrine states that it may use nuclear weapons if ICBMs are launched towards targets in Russia, to defend itself against a conventional attack that threatens the survival of the Russian state itself, or which threatens the ability to launch nuclear weapons. Those are all pretty sensible use cases (to the degree any reason to use nuclear weapons can be sensible). There's some question about what would count as a threat to the survival of the Russian state, but I don't think it could reasonably apply to anything happening in Ukraine, and again, I think if the Russian government was seriously pushing the interpretation that it could, it would want everyone to know that was a serious possibility. We'd be seeing signs of greater alertness. Things like submarine deployments, or ICBM launch vehicles being readied.
As for no one wanting a nuclear war, keep in mind that no one has agreed to retaliate in kind for Ukraines sake. There are a lot of people in Russia who do believe that they would be the only side using nuclear weapons
And that is probably true. I doubt any other nuclear power would be willing to start a war that would existentially threaten human civilization over a limited use of nuclear weapons in Ukraine. Hypothetically, it could absolutely happen, and if it didn't there would probably be some kind of ultimatum not to do it again, but I would personally doubt it because everyone kind of understands that nuclear escalation is a terrible idea. We know how close it came to disaster during the cold war, when nuclear doctrines were truly insane and terrifying.
There doesn't need to be the possibility of immediate nuclear retaliation for using nuclear weapons to be an incredibly bad idea. It might mean going from harsh sanctions from a few relatively wealthy countries to most of the world agreeing to a complete embargo on trade with Russia, for example. It might mean the US or other NATO allies deciding to risk limited engagement to try and destroy Russia's tactical nuclear capability in Ukraine and ensure the decision to use it isn't militarily rewarding. The world as a whole has a huge interest in making the decision to deploy nuclear weapons extremely punishing. Noone wants to go back to the world immediately after world war 2 where the only way to ensure you aren't hit with nuclear weapons is to have them yourself.
Besides, what would Russian nukes actually do in Ukraine? What would you drop them on? Do you drop them on cities and kill millions of people while economically destroying the region you're fighting for? Do you just drop them on the front line so that your own troops can advance a few miles through a now dangerous and contaminated region with completely destroyed infrastructure? Do you drop them on uninhabited wilderness just to show how super serious you are? None of the potential benefits seem worth the risks.