If the majority of your use of ecash is to pay LN invoices from one mint, and your are the only user of that mint, then your anonimity is the same as LN wallet to LN wallet.

If your wallet is custodial, your IP address is leaked to server and if you do not connect to your own node then more privacy is leaking.

If an ecash mint has several users, and several of them funding the mint via LN, when you make a LN payment from the mint (paying ecash to the mint) then your privacy is greater than in the above model of one user in the mint.

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That means a mint with a larger user base is beneficial to privacy. On the other hand, I love the idea of having mint's for (medium sized) communities, just in order to have a circular economy.

porque no los dos?

you can connect to as many mints as you want and trust, multi-mint payments have already been implemented and so you can settle LN invoices from multiple different ecash mints

#nuts