I've recently started using Perplexity and find that I've started using it for finding answers to specific questions, where I'll still use traditional search to find "a few sites on which I may be able to cobble together a useful set of information about <topic>".
So, for me, "search" has fragmented into two separate use cases, one of which is served by the new not-really-a-search-engine.
This is one of the few comments advocating for LLM search use that actually lines up with my experience trying to use it. It's pretty good for a narrow subset of my search queries, but it's totally useless for everything else.
I gave up on it because "two search tools instead of one" is just a really hard sell for me. When I go to search something, the keystrokes/hand motions are totally intuitive. Having two different patterns was annoying. StartPage works great for me. I have no reason to replace it, much less half-replace it with something that has only proven to be incrementally better at a few tasks. That's a matter of personal preference, though.
So, for me, "search" has fragmented into two separate use cases, one of which is served by the new not-really-a-search-engine.