[dotnet] Send data over cdp consecutively

[nvborisenko]

Description

This is respawn of 12591.

Motivation and Context

Fixes #12665

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)

Checklist

• I have read the contributing document.
• My change requires a change to the documentation.
• I have updated the documentation accordingly.
• I have added tests to cover my changes.
• All new and existing tests passed.