Add live profiling via DAP

[Copilot]

Implements profiling support for debugpy, enabling live performance analysis during debug sessions. Samples are streamed over DAP as individual call stacks suitable for flame graph visualization.

Core Implementation

• Profiling module (src/debugpy/server/profiling.py): Uses sys.setprofile() for accurate call stack capture at 10ms intervals (configurable)
• DAP extensions: startProfiling/stopProfiling requests, profilingData event stream
• Dataclass models: StackFrame, SampleBatch, ProfilingResult - no dicts except dynamic collections

Frame Deduplication Protocol

Reduces bandwidth 75-90% by sending frames once, then referencing by ID:

{
  "newFrames": {
    "12345": {"file": "/app/main.py", "line": 10, "function": "main"},
    "67890": {"file": "/app/utils.py", "line": 42, "function": "calc"}
  },
  "samples": [[12345, 67890], [12345]],
  "sampleCount": 2,
  "duration": 150.5
}

Frame IDs are stable hashes of (file, line, function). Client accumulates frame map, reconstructs full stacks from IDs.

Client Integration Pattern

const frameMap = new Map();

session.onDidReceiveDebugSessionCustomEvent((event) => {
  if (event.event === 'profilingData') {
    // Merge new frames
    Object.entries(event.body.newFrames).forEach(([id, frame]) => 
      frameMap.set(parseInt(id), frame)
    );
    
    // Reconstruct stacks from IDs
    const stacks = event.body.samples.map(ids =>
      ids.map(id => frameMap.get(id))
    );
    
    updateFlameGraph(stacks);
  }
});

Files

New:

• src/debugpy/server/profiling.py - profiler implementation
• tests/debugpy/test_profiling.py - test suite
• doc/PROFILING.md - API reference
• VSCODE_INTEGRATION.md - IDE integration guide

Modified:

• src/debugpy/_vendored/pydevd/_pydevd_bundle/_debug_adapter/pydevd_schema.py - protocol schemas
• src/debugpy/_vendored/pydevd/_pydevd_bundle/pydevd_process_net_command_json.py - request handlers
• src/debugpy/adapter/{clients,servers}.py - adapter integration

VSCode Python extension integration documented in VSCODE_INTEGRATION.md (repo: microsoft/vscode-python).

Original prompt

I want to add profiling support to this repo. i.e.

1. if someone has a debug session open in vscode connected to debugpy, they should be able to press a button to start profiling the process
2. profiler samples should be streamed back to the client over DAP
3. vscode should render them in a live-updating flame graph

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