Unfortunately 100 queries per day is quite low for LLMs, which tend to average 5-10 searches per prompt in my experience. And paying for the search API doesn’t seem to be worth it compared to something like a ChatGPT subscription.
The Google programmable search engine is unlimited and can search the web: https://programmablesearchengine.google.com/about/
You're not limited to 100 queries per day though. You're limited to 10,000 queries per day.