fix: use snake-case web search tool name

[wrightpt]

Summary

• call the web-search MCP tool by its discovered web_search_prime name
• update CLI, Code Mode, skill, and live-test examples
• add a non-live regression test for the exact tool name and argument mapping

Root cause

The Web Search MCP server currently advertises zai.search.web_search_prime, while the client hard-coded zai.search.webSearchPrime; direct search calls therefore failed tool resolution.

Validation

• npm run build
• npm test (40 passing)
• zai tools --no-vision --filter search -> zai.search.web_search_prime
• git diff --check