In my opinion, AJAX Search Pro is the best search plugin for LearnDash courses.
First of all, it provides lifetime pricing, which is very unusual for software purchases these days.
The User Interface looks a bit like an airplane cockpit, but that is because it is genuinely overflowing with features 🙂 Plus, the documentation is pretty good and you can usually get going quickly.
First of all, the search is high quality, and it is also very fast.
The indexing is near real-time, which means your latest content will be almost immediately searchable.
And it is especially useful for LearnDash video lessons (once you add the transcript) because the student can search across the entire text of all videos and go directly to the one they want to watch.