[Java] Tool-as-lambda 4.5: Add Java E2E integration test with replay proxy

[edburns]

Overview

Implement Phase 4.5 of #1810: add/extend Java E2E coverage proving inline lambda-defined tools work in a real session against the replay proxy.

Before coding

• Do not start any implementation work until this issue is explicitly assigned to the coding agent.
• Base branch for this work: edburns/1810-java-tool-ergonomics-tool-as-lambda.
• Read this plan file on the branch before coding:
  1810-java-tool-ergonomics-tool-as-lambda-remove-before-merge/1810-ignorance-reduction-for-implementation-plan.md

Ordering rule (important)

This issue starts only after 4.4 is merged; all Phase 4 issues are completed in listed order.

Relevant Phase 3 resolutions to apply

• 3.4 / 3.5: runtime schema/coercion behavior should match existing Java path.
• 3.9 snapshot strategy: start by reusing existing tool-definition replay snapshot(s); add a new YAML snapshot only if wire traffic differs.

Scope / deliverables

1. Add/extend Java E2E test(s) under java/src/test/java/com/github/copilot/e2e/ using inline lambda tool definitions.
2. Add/update test/snapshots/tools/* only if needed per 3.9.
3. Verify assistant behavior and tool side effects in-session.

Gating criteria

• E2E passes with expected invocation behavior and side effects.
• Snapshot choice follows 3.9 (reuse first, new snapshot only when required).

Constraints

• Follow existing Java E2E harness patterns in this repository.
• Keep scope limited to E2E integration for this feature.

Completion bookkeeping

When complete, update the checkbox for Phase 4.5 in:
1810-java-tool-ergonomics-tool-as-lambda-remove-before-merge/1810-ignorance-reduction-for-implementation-plan.md