J1 becames resident on January 1st, 2024, but still under treaty until the visa expiration. Left US after visa expired and had no US income after that. How should I file?

It depends on your situation.

You are considered a tax resident until the end of the year unless you become a resident of another country prior to the end of the year. So, if you moved back to Italy and that became your permanent home, you would not need to include income received from a foreign source after November 1, 2024.  Any income received prior to November 1, 2024 would be included on your US resident return. So, yes, in that situation, and by filing for only part of the year, you would be a dual status resident which that only means that you are a resident for part of the year and a non resident for another part of the year.  

If you did not become a resident of another country, then you would be considered a resident of the US for the entire year and need to include your income from worldwide sources for the entire year on your return. In this situation, you would NOT be considered a dual status resident. 

"Under the general rule, the residency ending date is December 31 of the calendar year in which you left the United States.

However, your residency ending date is the last day during the calendar year that you are physically present in the United States if, for the remainder of the calendar year:

• your tax home is in a foreign country (cf. Rev. Rul. 93-86); and
• you maintain a closer connection to that foreign country than to the United States (cf. Treas. Reg. § 301.7701(b)-2(d))." Residency starting and ending dates