As was the case last year, you no longer have to call unemployment to get a 1099 mailed to you. It will be sent automatically.
From the unemployment website ...
In January 2024, NYS DOL will automatically mail 1099-G tax forms to individuals who were paid benefits in 2023. These forms will be sent to customers' addresses on file.
Source: https://dol.ny.gov/unemployment/1099-g-tax-form