I would imagine that the government does host “full nodes” for Bitcoin and other crypto - it would make sense from a law enforcement/intel perspective since these are the nodes that validate all transactions and keep full databases of the blockchain.
Nothing to back this up, but I often wonder if Uncle Sam or another government wasn’t the one who came up with it in the first place - since despite what people say about its security, crypto is much easier to track than cash.
If they can, they will.