@Suresh Rajamani Thank you for the clarification. Based on the information you provided, it seems that you are having trouble searching against Edm.ComplexType and Collection(Edm.ComplexType) fields using the Chat Extensions REST API. However, you are able to search against other fields that are not of type Edm.ComplexType and Collection(Edm.ComplexType) using the Chat Extensions REST API.
It is possible that the issue is related to the Free Tier of Azure AI search. The Free Tier has some limitations, and one of them is that it does not support complex types. Therefore, you may not be able to search against Edm.ComplexType and Collection(Edm.ComplexType) fields using the Chat Extensions REST API if you are using the Free Tier.
To confirm if this is the case, you can try upgrading to a higher tier that supports complex types and see if the issue is resolved. If you are still having trouble after upgrading, please let me know and I will be happy to help you further.