Are there foreign transaction fees when the Apple Card is used in Italy?

No. See the following from the customer agreement: https://www.goldmansachs.com/terms-and-conditions/Apple-Card-Customer-Agreement.pdf

Transactions, returns and credits made in a currency other than U.S. dollars will be converted into U.S. dollars. We do not add any foreign exchange rate fee to these Transactions. The conversion will be performed by Mastercard International, the payment network associated with your Account (the "Network"). The Network follows its own methods for conversions that are subject to change. The conversion will occur on the day the Transaction, return or credit is processed by the Network, which may be different than the date of the Transaction, return or credit. As a result, the conversion rate may differ from the rate as of a Transaction date or the date a Transaction is posted on your Account.

Just for clarity Apple Card (Goldman Sachs Bank) does not charge a Foreign Transaction Fee or currency exchange fee. However, the Payment Network Operator (Mastercard, Visa, American Express etc.) will charge a foreign currency exchange. This is unavoidable unless the transaction is conducted in US Dollars. Some merchants may offer that, but be cautious of the merchant charging 5 to 10% extra. The PNO typically charges 3 to 5% for the currency exchange.