They probably don't even need a database anyway for data that is likely write once, read many. You could store the JSON of the meeting in S3. It's not like people are going back in time and updating meeting records. It's more like a log file and logging systems and data structures should be enough here. You can then take that data and ingest it into a database later, or some kind of search system, vector database etc.
Database connections are designed this way on purpose, it's why connection pools exist. This design is suboptimal.
What you describe makes sense, of course, but few can build it without it being drastically worse than abusing a database like postgres. It's a sad state of affairs.