Hey!
I am afraid this will not be possible. We do not have a way to integrate federated search within the community - it would only work the other way around (so search community content on your public docs site). We currently only offer federated community search with a number of specific vendors, e.g. Zendesk.
I am not sure what the limitation here is, but could be that the structure of the data needs to be in a certain format in order to be able to used for our community search. The least that I can do for you is to share your vision with the product team - maybe there will be a way to connect an external api for this purpose in the future then.