[demo split #4449] 5/5 — Add instrumentation overhead benchmarks

[allspain]

DEMO — split of #4449. This is one of 5 stacked draft PRs that breaks
#4449 — Add Live Debugger package
into reviewable increments. Original PR is untouched. This stack is for
demonstrating tooling (jj split for the surgery, gh for the stack);
all of the underlying code is Thomas Watson's work and credited via
Co-authored-by: trailers.

Stack

1. [demo split #4449] 1/5 — Foundation: expose core hooks for the live debugger package #4532 — Foundation — expose core hooks for the live debugger package (12 files / +56-10)
2. [demo split #4449] 2/5 — Add @datadog/browser-debugger package #4533 — Package — add @datadog/browser-debugger (25 files / +6433)
3. [demo split #4449] 3/5 — Extend e2e framework for the debugger package #4534 — E2E framework — extend test framework for the debugger package (12 files / +129-8)
4. [demo split #4449] 4/5 — Add debugger e2e scenarios #4535 — E2E scenarios — add debugger e2e scenarios (3 files / +318-2)
5. [demo split #4449] 5/5 — Add instrumentation overhead benchmarks #4536 — Perf benchmarks — add instrumentation overhead benchmarks (12 files / +1222-9) ← you are here

Each PR's base branch is the previous PR's head, so reviewing in order is
the intended path. Stack constructed with jj:
all 4 commits from #4449 were squashed into one change, then peeled into 5
with jj split <paths>, then pushed with jj git push.

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What this PR contains (5/5 — Perf benchmarks)

Performance benchmark measuring the runtime overhead of debugger
instrumentation hooks. Independent of the E2E scenarios in PR 4 in concept,
but stacked behind it for review-order linearity.

Changes

• test/apps/instrumentation-overhead/ — webpack test app with
  instrumented vs uninstrumented function variants.
• test/performance/scenarios/instrumentationOverhead.scenario.ts —
  benchmark scenario stress-testing 10M function calls to measure hook
  overhead.
• test/performance/createBenchmarkTest.ts — extended with
  instrumented_no_probes and instrumented_with_probes scenario configs
  and a dedicated injectDebugger function.
• test/performance/profiling.type.ts, server.ts — wiring.

12 files, +1222 / -9.

Tests

yarn build:apps && yarn test:performance.

[github-actions]

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[datadog-datadog-prod-us1]

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

🎯 Code Coverage (details)
• Patch Coverage: 100.00%
• Overall Coverage: 76.66% (-0.01%)

_{This comment will be updated automatically if new data arrives.
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