I've just deployed the ApiFeatureUsage extension to Beta Labs for testing. If an API client (e.g. a bot or a user script) sets a unique User-Agent or Api-User-Agent header, a summary of deprecated API features hit by that client may be fetched from Special:ApiFeatureUsage[1] or from the API itself.[2]
Please try it out, and report any issues in Phabricator using the MediaWiki-extension-ApiFeatureUsage project. If things look good after testing I'll be looking at getting it deployed to production in the next month or so.