That NY Times article is a terrible take. The only evidence of conscripts being present in the Ukraine are from captured Russia personnel. It's not surprising to hear POW claiming they didn't want to invade Ukraine, they were sent against their will, and so on. It is understandable and a way to elicit sympathy from your captors.
Putin himself has said that no conscripts have been deployed to the Ukraine and nor is there any plan to do so. You can claim he's lying and trying to hide Russian losses, but conscripts were deployed to Chechnya and there was no denial of their deployment there.
I've said multiple times that in this day and age countries tend to be accurate about their own deaths and exaggerate the numbers of enemy killed. We've seen that in every recent modern conflict including Galwan, the Azeri war and the 2014 Donbass war. We all know how crazy Indian claims were for numbers of PLA soldiers killed, but the number of their own dead was pretty accurate from the start. Soldiers have families and you can't hide someones death from them even in a dictatorship.
By feeding this myth that Russian soldiers are dying in their thousands they're actually making it worse for Ukraine.