I've configured Claude to use their search MCP instead of vanilla Websearch and it has been great. I think it's subscriber-only but I've been on the $5/mo plan for a while and have never him my limit. I might bump up to a higher plan just out of how philosophically refreshing they are as a service. https://github.com/kagisearch/kagimcp
I also confirm the $5 you get is only promotional credit.
I tested on my local LLM chat via Open WebUI, 2 requests from that cost $0.02 (so $4.98 left), and after my monthly Kagi renewal an hour ago, it did not reset, I am still on $4.98.
You are probably better off using Kagi Assistant anyways, as you get $10 there on the $10 Professional plan.
For local LLM web searches, to save on cost I will stick with the Brave Search API which gives you $5 free every month.