agentic_tools_literal() already contains a custom web_search tool.
agentic_tools_with_web() adds the Anthropic server-side web_search_20250305
tool (also named web_search). Combining them caused Anthropic to reject
every agentic request with 'Tool names must be unique.'
agentic_tools_all() now calls agentic_tools_literal() directly. Connector
tools splice in as before. The web_search-only variant (agentic_tools_with_web)
is unchanged for callers that specifically want native search without connectors.