Earlier quoted context omitted.
For search, use Kagi. You don’t have to use their AI products at all to just use search.
If Kagi made a cheaper "no AI" tier I would be happy to subscribe. AI is costly to run, so even if you don't use the AI it's priced into your subscription fee - you're paying for an expensive product you don't want or use. e: according to Kagi's pricing page they do have a 'no AI' tier, but it limits your number of searches to 300/month. Seems like a totally arbitrary limitation, but its still better than forced AI.
The only extra costs are if you use the (opt-in optional) AI Assistant which is a web UI to access various models for chatting purposes. As an aside, they recently updated this UI so it’s actually usable as a ChatGPT or Claude alternative.