Cooperative Interoperability is when the platform explicitly works with third parties to enable them, mostly because the platform sees the benefits of adding capability without paying to develop it (in fact, it could be their primary revenue stream, as with Stripe or anything else in the API economy). We may be familiar with these as an “API marketplace” or “plugin ecosystem”, but also this happens on a “spec” level with major languages, protocols, and file formats.
Adversarial Interoperability is when the platform does NOT explicitly want third parties to connect for whatever reason, whether it is about control of data or of revenues or of content available on a platform, BUT, crucially, third parties are still able to interop with it anyway. Plaid, the fintech unicorn still mostly operates via screen-scraping, as do Mint and Quicken.
Indifferent Interoperability is when the platform doesn’t care, e.g. a fridge maker doesn’t care what magnets you put on the door. Usually platforms here claim they are “unopinionated”, but I don’t think this attitude lasts forever.