Accessing NBA via the Tooling API
The Tooling API provides a way to get information about Action Strategies. I’m more familiar with the Metadata API, but in general Salesforce is trending towards the Tooling API as a more flexible, granular tool, and this is likely to increase. For performance reasons, metadata API deploys and retrieves will often trigger a recompilation of all of an org’s Apex. (This is controlled by a setting in Apex Settings called “Perform Synchronous Compile on Deploy” which is on by default in many orgs). The recompilation can make the mdapi deploy/retrieve too slow for quick data calls of the sort you’d want for your apps. So Tooling API is the way to go.
/services/data/v45.0/tooling/sobjects/RecommendationStrategy/describe
You can provide a recordId and get all the information about the record with:
/services/data/v45.0/tooling/sobjects/RecommendationStrategy/0sgB000000003PcIAI/
This returns a json data structure that’s visualized here in workbench:

To retrieve a list of strategies, use Select query language. For example:
/services/data/v45.0/tooling/query/?q=Select+id,MasterLabel,DeveloperName+from+RecommendationStrategy

As a tip, it is considerably easier to play with this api if you install the Salesforce Workbench Tools for Google Chrome. Just go to a page that’s logged in to your org and then click this button in the toolbar.