The Connect API is meant to be used in situations where you want to do posts in Apex: Visualforce, Apex code triggers, and Lightning. You would not ordinarily write a custom REST API service when there is a viable, non-custom way to perform the same action. Stated more simply, use the Connect API when you're already using Apex and need to post a Chatter ...
ConnectApi does a callout using sessionId, as of now lightning session is not API enabled and that might be failing your code to like the post.
You can manually insert FeedLike
INSERT new FeedLike (FeedItemId = FeedEntityId);