Is it possible to use the State and Country/Territory picklists feature for custom objects? When I searched online it says that State and Country/Territory picklists adds picklists to standard address fields to standard objects -account,contact,lead,order

The State and Country/Territory features is designed for standard objects and isn't directly applicable to custom objects. However, you can work around this limitation by creating custom fields and using validation rule or Apex.

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I hope this helps !