Fix disk space issue in .NET PR creation by implementing sparse checkout

[Copilot]

The Submit-AzureSdkForNetPr.ps1 script was performing a full clone of azure-sdk-for-net (several GB), causing the pipeline to run out of disk space and timeout.

Changes

• Replace full git clone with sparse checkout using cone mode
• Fetch only the eng/ directory (contains Packages.Data.props and packages/http-client-csharp/)
• Use shallow fetch (--depth 1) to minimize history

# Before: Full clone (~several GB)
git clone "https://github.com/$RepoOwner/$RepoName.git" $tempDir

# After: Sparse checkout (~185MB)
git init $tempDir
git remote add origin "https://github.com/$RepoOwner/$RepoName.git"
git sparse-checkout init --cone
git sparse-checkout set eng/packages/http-client-csharp eng
git fetch --depth 1 origin $BaseBranch
git checkout $BaseBranch

Original prompt

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This section details on the original issue you should resolve

<issue_title>Update .NET PR failing</issue_title>
<issue_description>For the last several runs, the update .NET PR script has timed out:
##[error]System.IO.IOException: No space left on device : '/usr/local/vss-agent/4.264.2/_diag/Worker_20251123-215819-utc.log'
at System.IO.RandomAccess.WriteAtOffset(SafeFileHandle handle, ReadOnlySpan`1 buffer, Int64 fileOffset)
at System.IO.StreamWriter.Flush(Boolean flushStream, Boolean flushEncoder)
at System.Diagnostics.TextWriterTraceListener.Flush()
at Microsoft.VisualStudio.Services.Agent.HostTraceListener.WriteHeader(String source, TraceEventType eventType, Int32 id) in /mnt/vss/_work/1/s/src/Microsoft.VisualStudio.Services.Agent/HostTraceListener.cs:line 131
at System.Diagnostics.TraceSource.TraceEvent(TraceEventType eventType, Int32 id, String message)
at Microsoft.VisualStudio.Services.Agent.Worker.Worker.RunAsync(String pipeIn, String pipeOut) in /mnt/vss/_work/1/s/src/Agent.Worker/Worker.cs:line 102
at Microsoft.VisualStudio.Services.Agent.Worker.Program.MainAsync(IHostContext context, String[] args) in /mnt/vss/_work/1/s/src/Agent.Worker/Program.cs:line 54
System.IO.IOException: No
,##[error]The job running on agent azsdk-pool 1 ran longer than the maximum time of 60 minutes. For more information, see https://go.microsoft.com/fwlink/?linkid=2077134
,##[warning]Agent azsdk-pool 1 did not respond to a cancelation request with 00:05:00.
Pool: azsdk-pool
Agent: azsdk-pool 1
Started: Yesterday at 1:58 PM
Duration: 1h 4m 59s

Job preparation parameters
Parent pipeline used these runtime parameters

https://github.com/microsoft/typespec/blob/main/packages/http-client-csharp/eng/pipeline/publish.yml#L126

When seeing the initial run it said the device was low on disk space. We may need to do a sparse checkout instead.</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Update .NET PR failing #9081

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