Thank you for the suggestions. Excluding false positives and the typical hallucinations LLMs exhibit, exa.ai was useful and would often give me what I asked for. Perplexity, not as much. Searx seems interesting; I will certainly toy with it.
Case 2: When searching three standalone exclamation marks, I get the "No results found" message on both search engines. What's interesting is that Qwant successfully displays a preview of the Wikipedia article of the band with the name "!!!"