I need to find my AirPods by serial number

A serial number cannot be used to locate any Apple devices, AirPods, iPhone, or otherwise.

That’d be a security catastrophe, as it’d let anybody track a device knowing just that info.

Bluetooth signal strength (short range) and Find My (local or relay via nearby Apple devices) are the available options.

As far as I know, you cannot.

https://support.apple.com/en-us/HT207581