[demo split #4449] 2/5 — Add @datadog/browser-debugger package

[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) ← you are here
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)

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 (2/5 — Package)

The @datadog/browser-debugger package itself: the full probe execution
pipeline. Builds on the core changes from PR 1.

Changes

• domain/api.ts — Core instrumentation hooks (onEntry, onReturn,
  onThrow) that execute probes when instrumented functions are called,
  including condition evaluation, snapshot capture, template message
  rendering, and rate limiting.
• domain/activeEntries.ts — Tracks per-probe execution stacks for
  correlating entry/return/throw events.
• domain/probes.ts — Probe lifecycle management (add, remove, clear)
  with per-probe and global snapshot rate limiting.
• domain/capture.ts — Deep value capture for arguments, locals, return
  values, and thrown errors with configurable depth/size limits.
• domain/expression.ts — Expression compiler that parses JSON
  expression trees into executable functions.
• domain/condition.ts — Probe condition evaluator with caching.
• domain/template.ts — Template segment compiler/evaluator for dynamic
  probe messages.
• domain/stacktrace.ts — Stack trace capture from Error objects.
• domain/deliveryApi.ts — Polling-based probe delivery client.
• transport/startDebuggerBatch.ts — Reuses
  @datadog/browser-core's batch/flush infrastructure.
• entries/main.ts — Public API surface (datadogDebugger.init()),
  exposes $dd_entry/$dd_return/$dd_throw/$dd_probes on globalThis.

Specs included for: api, capture, condition, deliveryApi,
expression, probes, stacktrace, template, entries/main.

25 files, +6433 / -0.

Tests

Unit tests run with yarn test:unit --spec "packages/debugger/src/**/*.spec.ts".

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[datadog-datadog-prod-us1-2]

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

🎯 Code Coverage (details)
• Patch Coverage: 71.76%
• Overall Coverage: 76.68%

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