I don't use their API, but the search works for my scenarios. I'm not an heavy commenter, but it never failed in their app (which is supposedly Electron based) and Firefox for me.

Did you open tickets for these? Some Notion developers frequent here I believe, maybe you can reach them if they provide contact information?

I always found it beneficial to reach-out to provider/developer. The results were not positive all the time, but at least I managed to add an entry to their bug tracker, and the problems are solved 99% of the time, after some time.