Well, Google did say 'Bard is an experimental conversational AI service'. Not even ChatGPT or Bing AI are any more accurate or reliable and both are also experimental and in preview. [0]
I can confidently say that this stock drop is a typical over-reaction from the markets. Today, neither AI is ready to even challenge or replace search engines due to their hallucination issues and LLMs like ChatGPT are unable to cite their sources or even explain them.
If you cannot trust the output from a chatbot or an AI to generate correct or factual information, then it has little chance in being useful enough to be a reliable search engine replacement.
[0] https://www.theverge.com/2023/2/7/23589536/microsoft-bing-ai...
I don't know that people are reacting to the error per se, so much as they're reacting to where they saw it: in a major, high-glitz public announcement. Like NPR quotes others, the human beings who prepared the announcement could've googled to make sure they didn't demo a product working as unintended.
I think people understand AI's current limitations. What they've lost confidence in is Google's judgement, not Bard's.