Automating API SDK testing that supports multiple programming languages

I have a requirement to automate testing for an API SDK written in 5 programming languages. The SDK is similar to jira SDKs. Writing Tests across all 7 languages will lead to duplicating testing logic in all programming languages.

I want to find a way to call the SDK methods (which are basically API calls internally) from different programming languages in any one language (preferably python) and compare the response with the public api call (SDKs being wrappers for these public APIs.) So far I have thought of creating a rest server in all languages (wrapper APIs over the SDK methods) and call these wrapper APIs to get the response and then proceed with comparison

I am wondering how the industry soles this problem in general and if there is a simpler solution to this problem which does not involve creating wrapper APIs for SDKs from different languages.