The visa gives immigration status; it does not create a special tax holiday. If you become Italian tax resident, Italy can tax worldwide income unless a treaty or special regime changes the result.
Tax residency trigger
Italy generally treats you as tax resident if, for most of the tax year, your registered residence, domicile, or habitual abode is in Italy. For practical planning, anyone living in Italy for more than 183 days should assume Italian tax residency is a serious possibility.
Regular tax picture
Resident individuals pay progressive IRPEF, plus regional and municipal surtaxes. Remote employees and self-employed workers may also face social-security questions. The answer depends on employment status, employer country, EU coordination rules, and treaty coverage.
Special regimes
Some inbound workers consider Italy's impatriate regime or flat-tax regimes, but eligibility is specific and has changed in recent years. A digital nomad visa approval does not automatically qualify you. Treat special-regime analysis as a separate tax project before you move.
US citizens
US citizens remain subject to US worldwide taxation. Foreign Earned Income Exclusion and Foreign Tax Credit planning can reduce double taxation, but Italy's tax-residency and social-security treatment should be modeled before committing to a lease.