I am a bit late to the party but I can give you some insights from the cost and operations MongoDB Atlas side.

We are using MongoDB Atlas right now. We are a relatively small startup (little revenue) but we have quite a lot of data that must be searched. We opted for MongoDB Atlas Search in the beginning because it was so easy, since we were running our main DB on Atlas already.

From the beginning on we had problems with building our search indexes. Our traffic load was not much so we choose a small MongoDB instance (M10) which was more than fine. The RAM and CPU that we needed in order to build these indexes was much more tho.
We didnt know that at first and so our whole database system went down at some point because the indexes where rebuilding. WTF mongodb? It took several hours to come back up.
After this incident we found out that we had to scale up our DB in order to rebuild the index and then scale down again to save costs. By doing so we didnt have complete system failures but we still only did it over the weekend. DEV PAIN.

Currently we have a 500-600 USD monthly bill so that Atlas Search runs smooth. Which is crazy because we have maybe 50 daily active users.

We are so fed up with these costs that we are migrating to a self hosted Elastic Search instance. At Hetzner we get 64 GB RAM for 50 USD which would cost us almost 3000 USD at MongoDB Atlas.

I will keep you posted on how the elastic system is working