Used Monzo all over Lima but restricting use to chains and established stores. Although most places show the Visa logo only, nearly all accept Mastercard too.
You are nearly always required to sign, even though you have entered a correct PIN.
When paying, tell them it’s a debit card (debito) or they’ll assume credit card, which in Peru requires you to give them your passport number. Having said that, they do not check that it is correct…
Many restaurants put the amount through at 20% more, but this settles down to the correct amount after a few days.