Can they trace the BTC back to the original sender.
Yes, a sufficiently motivated nation-state has the resources to attempt this. Individuals can only make it extra difficult for them.
The blockchain data doesn’t identify individuals or businesses explicitly but is public. A sufficiently resourced agency of a nation-state can combine this blockchain information with external sources of information and may thus be able to infer underlying business relationships and participation in real-world transactions.
Avoiding address reuse and running money through mixers and multiple exchanges etc obviously makes this much much harder and more expensive for the nation-state’s agencies, and more private for the transaction participants. But nothing can be 100% private.
I expect most people buying something, for their own use, whose purchase is a misdemeanour, would not worry much.
The next leader of Hezbollah, buying arms and ammunition, say, might be expected to be concerned about this sort of thing.
