Pretty much agree with Super Testnet as far as I can see (assuming you're not using custodial wallets or LSPs which changes the privacy assumptions). If you want to obscure where the senders payment went from the sender on Monero send your entire balance back to yourself a few times. At random times preferably.

It is actually more nuanced than the fueding factions usually make it out to be.

What amounts are hidden for each one and who sees them depends. Monero fees are exposed to the general public, but hides the actual transaction amount between sender/receiver from everyone else. Lightning exposes at least partial fees and amounts to limited third parties - routing nodes - but hides fees and transaction amount from the general public.

I think the best privacy, in concept, for digital cash would be hiding everything completely using a ZK scheme + offchain (to reduce exposing what little information is left). I don't think either Monero or Lightning meet that yet, but they're both constantly improving.