Is there a way to use the v2 api to get the column names for a given connection/database/schema/table similar to /tspublic/v1/connection/fetchLiveColumns? I am trying to use the search connection API but cannot figure out how to use it to get the same results

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I see this in the search connection API

To get a specific database, schema, table, or column from a connection object, define the object type in data_warehouse_object_type and object properties in the data_warehouse_objects array. For example, to search for a column, you must pass the database, schema, and table names in the API request. Note that in the following example, object properties are set in a hierarchical order (database > schema > table > column).

Does this not help? It should give similar results, Do you only get the objects that are present in your connection here?