Subagents cannot use WebSearch/WebFetch tools even when parent session has access

Bug Report

When spawning subagents via the Agent tool, the subagent is unable to use WebSearch or WebFetch tools even when the parent Claude Code session has those tools available.

Steps to reproduce

1. In a Claude Code session where WebFetch/WebSearch are available to the main agent
2. Spawn a subagent (e.g., type: Explore or general-purpose) with a research task that requires web access
3. The subagent repeatedly reports permission denied for WebSearch/WebFetch

Expected behavior

Subagents should inherit the tool permissions of the parent session, or at minimum have access to web tools when the parent does.

Actual behavior

Subagent reports: "I don't have permission to use WebSearch or WebFetch in this session" and cannot complete web research tasks, even when the same tools work fine in the parent session.

Impact

Blocks delegation of any web research tasks to subagents, forcing the parent agent to do all web lookups itself and defeating the purpose of parallel subagent execution.