After all, until quite recently, chess engines really were quite mechanically search engines too.
> can follow logical rules
This is not their strong suite, though. They can only follow through a few levels on their own. This can be improved by agent-style iterations or via invoking external tools.
As mentioned, there are good ways to counter this problem (e.g. writing a plan and then iteratively going over those less-complex ones, or simply using the proper tool for the problem: use e.g. a SAT solver and just "translate" the problem to and from the appropriate format)
Nonetheless, I'm always open to new information/evidence and it will surely improve a lot in a year. As for reference, to date this is my favorite description of LLMs: https://news.ycombinator.com/item?id=46561537
What I will argue is that the LLMs are not just search engines. They have "compressed" knowledge. When they do this, they learn relations between all kinds of different levels of abstractions and meta patterns.
It is really important to understand that the model can follow logical rules and has some map of meta relationships between concepts.
Thinking of a LLM as a "search engine" is just fundamentally wrong in how they work, especially when connected to external context like code bases or live information.