Postgres isn't a replacement for elastic. You CAN get full text search working in postgres, and for very basic use cases it's good enough, but it's vastly inferior to elastic in terms of features and performance.
Exactly. These "extensions".. they are good, but, far from being replacements for dedicated products, the quality of which customers have come to expect.
This is a very typical, and pretty bare-bones stack. Almost any production grade webapp above a minimal threshold of complexity will have database, cache, and search.