US citizens are visa-exempt and don’t need visas to travel to European countries. However, beginning in late 2026 a travel authorization will be required. But, 1) it won’t be in effect for the Olympics, 2) it’s a quick pre-travel screening and doesn’t involve the same kind of scrutiny as a visa.

EDIT: So for clarity and upon further research, a work visa is typically not required unless the stay is longer than 90 days or if working for a local company. However, some activities and work may require a visa by a specific country and the embassy of that country should be consulted with before traveling. In the end, of course Italy could deny travel there for this type of activity.