It's good that you are successful to use the library offline, which proves that the library is working OK and fulfilling its task successfully. What happens in IoT is beyond the library's reach.
If the motor is not responding when being controlled online, the bug must be in your IoT code.
Even the code is working on Nano_33_IoT, it can't 100% work on Nano_RP2040_Connect.
Unless you post the code here and hopefully someone will help, only you can debug and know what's wrong with your code, by including certain debugging code to verify the Servo commands correctly reach the board and the board issues the correct commands to the Servo.
Good Luck,