I am really not sure at first place how this Web Service was created, as my team has inherited this webMethods code from another team.
If there is any way to check how this Web Service is created, please help to know so that my team can have a look at it.
As you have mentioned I have not seen any option while creating a new Provider - Web Service Descriptor, where to define or select the “Contract-First” OR “Code-First”.
I think you are trying to say is:
Contract-First: Is something the WSDL file is created first and then imported into webMethods code to create Web Service Descriptor.
Code-First: In this case, the Flow Services are already developed, and using that we create a Web Service Descriptor.
Let me know if my understanding is correct?