♻️ Rename E2E intake server to Datadog proxy

[watson]

Motivation

The E2E "intake" server now handles more than captured SDK event intake. It also acts as the local proxy for Datadog-facing endpoints, including debugger probe delivery. Calling the whole server "intake" made the framework API misleading.

Changes

• Rename the shared E2E server from intake to datadogProxy.
• Split the Express server app from the test control API, so endpoint serving and test-only state manipulation are separate.
• Rename serverApps/intake.ts to serverApps/datadogProxy.ts.
• Add a debugger-specific Datadog proxy augmentation for the debugger Delivery API route and control plane.
• Expose datadogProxyControl in E2E test context and update existing debugger scenarios to use it directly.

Test instructions

• yarn lint
• yarn typecheck

Checklist

• Tested locally
• Tested on staging
• Added unit tests for this change.
• Added e2e/integration tests for this change.
• Updated documentation and/or relevant AGENTS.md file

[watson]

• ✅ Add debugger E2E coverage for delivery lifecycle #4738
• ♻️ Rename E2E intake server to Datadog proxy #4737 👈 (View in Graphite)
• main

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[cit-pr-commenter-54b7da]

Bundles Sizes Evolution

📦 Bundle Name	Base Size	Local Size	𝚫	𝚫%	Status
Rum	171.86 KiB	171.86 KiB	0 B	0.00%	✅
Rum Profiler	7.88 KiB	7.88 KiB	0 B	0.00%	✅
Rum Recorder	21.21 KiB	21.21 KiB	0 B	0.00%	✅
Logs	54.31 KiB	54.31 KiB	0 B	0.00%	✅
Rum Slim	129.69 KiB	129.69 KiB	0 B	0.00%	✅
Worker	22.96 KiB	22.96 KiB	0 B	0.00%	✅

[datadog-official]

🎉 All green!

🧪 All tests passed
❄️ No new flaky tests detected

🎯 Code Coverage (details)
• Patch Coverage: 100.00%
• Overall Coverage: 76.72% (+0.00%)

_{This comment will be updated automatically if new data arrives.
🔗 Commit SHA: 4964263 | Docs | Datadog PR Page | Give us feedback!}