Fix Process standard stream examples to avoid resource leaks and add ownership remarks

[Copilot]

Process.StandardOutput/StandardError examples assigned the stream to a local variable without disposing it, creating a resource leak. Documentation also lacked any explanation of stream ownership semantics.

Snippet fixes

Inlined stream access to eliminate undisposed StreamReader/StreamWriter variables:

// Before (leak: reader never disposed)
StreamReader reader = process.StandardOutput;
string output = reader.ReadToEnd();

// After
string output = process.StandardOutput.ReadToEnd();

Applied to all three language variants (C#, VB, F#) for both StandardOutput and StandardError examples.

Documentation remarks

Added [!IMPORTANT] notes to StandardOutput, StandardError, and StandardInput in Process.xml clarifying:

• Synchronous access transfers stream ownership to the caller — Process.Dispose() will not close it
• BeginOutputReadLine/BeginErrorReadLine retains process ownership and disposes on process disposal

[dotnet-policy-service]

Tagging subscribers to this area: @dotnet/area-system-diagnostics-process

[LBensman]

@adamsitnik, I think Copilot got a little too excited here and didn't understand the issue and technically the "fix" is worse. Instead of adding using to stream/reader to guarantee disposal, it instead removed the variable, so now it can't even be marked properly as owning the disposable instance.

As I stated originally in the reporting issue, documentation fix is one option. But Copilot did demonstrate exactly how unaware developer would make a mistake (chaining and reading directly, without acknowledging having taken ownership). So, I'd re-evaluate the weird contract and consider to have Process.Dispose() to also dispose the associated streams/readers.

But at minimum, for documentation purposes, Copilot should've created using StreamReader reader = process.StandardOutput;