[release/v7.5] Set standard handles explicitly when starting a process with -NoNewWindow

[pwshBot]

Backport of #25061 to release/v7.5

Triggered by @TravisEz13 on behalf of @daxian-dbw

Original CL Label: CL-General

/cc @PowerShell/powershell-maintainers

Impact

Choose either tooling or Customer impact.

Tooling Impact

• Required tooling change
• Optional tooling change (include reasoning)

Customer Impact

• Customer reported
• Found internally

When using Start-Process with -NoNewWindow, the output of the process will be messed up. See the "expected behaviors" and "actual behaviors" in the original issue.

Regression

• Yes
• No

Introduced in 7.5

Testing

Added a test

Risk

• High
• Medium
• Low

[High/Medium/Low. Justify the indication by mentioning how risks were measured and addressed.]

[daxian-dbw]

Describe how this issue impacts customers, citing the expected and actual behaviors and scope of the issue. If customer-reported, provide the issue number.

Original issue: #24986
When using Start-Process with -NoNewWindow, the output of the process will be messed up. See the "expected behaviors" and "actual behaviors" in the original issue.

[TravisEz13]

@daxian-dbw this is consistently failing the build.

[TravisEz13]

/azp run PowerShell-CI-linux-packaging, PowerShell-Windows-Packaging-CI

[azure-pipelines]

Azure Pipelines could not run because the pipeline triggers exclude this branch/path.

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