Full STDERR log

[AArnott]

Is your feature request related to a problem? Please describe.

We still have customer reports of failing MCP servers in VS, and while we get the stderr tail due to your fix for #362, it's not enough.
In one case, this is all we get:

Server's stderr tail:
    'Q:\\.tools\\.npm\\_npx\\0a405bf06814f506\\node_modules\\@azure\\identity\\dist\\commonjs\\credentials\\defaultAzureCredential.js',
    'Q:\\.tools\\.npm\\_npx\\0a405bf06814f506\\node_modules\\@azure\\identity\\dist\\commonjs\\index.js',
    'Q:\\.tools\\.npm\\_npx\\0a405bf06814f506\\node_modules\\tedious\\lib\\connection.js',
    'Q:\\.tools\\.npm\\_npx\\0a405bf06814f506\\node_modules\\tedious\\lib\\tedious.js',
    'Q:\\.tools\\.npm\\_npx\\0a405bf06814f506\\node_modules\\mssql\\lib\\tedious\\connection-pool.js',
    'Q:\\.tools\\.npm\\_npx\\0a405bf06814f506\\node_modules\\mssql\\lib\\tedious\\index.js'
  ]
}

Node.js v20.17.0

There's probably some rich information in this if we could only get more of it.

Describe the solution you'd like

For this, and other reasons we'd very much like to get the STDERR pipe itself, or at least a chance to get a copy of it. It can be streaming, so you don't have to indefinitely buffer. But we'd like to have total control over how much we buffer or log to a file for analysis.

Describe alternatives you've considered

Just increase the size of the buffer included in the exception you throw. But I reject this idea as a total solution because there will always be times when the tail size you choose isn't enough (though it might be an improvement in its own right).