This module takes POST requests, so I'd just send it as part of the request body, but when it comes to deserialising it, I'm not really sure what to deserialise it to as everything seems to assume primitive values, e.g. strings, integers, etc. when it comes to setting the parameter type.
The Action API is generally based around a "form" model, and submission of complex data structures is generally discouraged. If you really need to do so anyway, you might accept data as a JSON string, or possibly you might use the "templated parameters" added in 1.32.
MediaWiki now (since 1.34) also has a REST API. There the convention is to accept JSON data structures via POST or PUT, ideally validated against a JSON Schema of some sort.