[FEATURE] Support `additionalContext` in Stop hook output

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Stop hooks currently support 'decision: "block"' with a 'reason' field, but there's no way to inject structured context into the agent's conversation, unlike PreToolUse hooks which support "hookSpecificOutput.additionalContext".

This makes it difficult to build background tools that surface findings to the agent between turns.

Proposed Solution

Support additionalContext (or hookSpecificOutput.additionalContext) in Stop hook output, matching the behavior already documented for PreToolUse, PostToolUse, SessionStart, and other hook types.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Developer tools/SDK

Use Case Example

I am running a daemon that analyzes changes in the background and injects these into context as the agent is working. When the stop hook fires, we check for completed tasks and want to inject findings into the agent's context so it can act on them.

Currently, the only field that reaches the agent is 'reason'. I've tested:

Field | Reaches agent?

• "reason" (top-level) | Yes
• "additionalContext" (top-level) | No
• "hookSpecificOutput.additionalContext" | No
• stderr | No

We're using "reason" as a workaround, but it's semantically wrong. "reason" is meant
to explain why the agent should continue, not to provide review feedback or context.

Additional Context

Related: #24244, #16227 — similar requests for richer Stop hook output