But the sender (presumably who sells you btc) must know about your channel. If it is private, you will send him a routing hint. This could be avoided if you open a parallel public channel to the same LSP. Also, force closure may reveal that it is a channel. Not sure about the taproot channels in this context. Finally, at least lnd (so Blixt too, not sure about other implementations) may happily sweep and combine various UTXOs after forced closure, this also leaks some information.