as far as i know, the limiting factor is not the number of characters in your URL. when i read the thread you referenced, it looks to me like what they’re saying is that any character limit in the browser would have existed in the past with Internet Explorer, which is a browser hardly anyone uses any more. otherwise, limits are more likely to be enforced by the server and would just depend on how the server is set up.
that said, why do you need to get 333+ place ids into a particular request? are you trying to get details of all those places from /v1/places/{id}, or are you trying to get observations from a set of places from /v1/observations?place_id=[list of places]?