You couldn't break up the AI search engine and the traditional search engine. They're basically one and the same. The AI search engine relies on the index. The index uses AI in various places. The "traditional" side has long used AI for query understanding, ranking, and fact extraction.
Legislators don’t (and should not) care about your implementation. The old company will be banned from using ai for their search for x years the new company will get employees and assets including source code to startup the new entity.