No, if the library is just written using the common features of all platforms supported by the Arduino IDE this shouldn't be a problem.
I guess you checked the obvious: Not using the same filenames as you did on the Nano IoT 33, not having filled the complete chip in a previous write, etc.
If you setup is on a breadboard it might be good to decrease the SPI speed. The SAMD of the Nano isn't able to provide the configured 50MHz, the ESP32 might reach that. Frequencies above about 4MHz aren't suitable for breadboard setups.
Change the speed in the SerialFlashChip.cpp near the top of the file (SPICONFIG).