Looking for how to write verbose or debug string messages to PowerShell runspace without C# Cmdlet definition

Note:

• This is not a complete answer, because it has severe limitations - though it may work for specific use cases.

• The original form of this answer used since-deprecated PowerShell SDK method .CreateNestedPipeline(), which cannot be used anymore if you're writing your code against the PowerShellStandard library for cross-platform and cross-edition compatibility (code that should run in both Windows PowerShell and PowerShell Core, on all supported platforms).
  Chris (the OP) himself found a compatible alternative, which the current form of this answer is based on.

The challenge is to write to the invoking pipeline's output streams (as you've observed writing via Console is unrelated to PowerShell's output streams and prints directly to the console, with no ability to capture or redirect such output in PowerShell).

While you can obtain a reference to the invoking runspace, there is no way I know of to obtain a reference to the running pipeline.

Using the invoking runspace you can write to PowerShell's output streams via a new pipeline, but that comes with severe limitations:

• You cannot directly write to the caller's success output stream (1) that way; that is, while you can call cmdlets that target the other streams, such as Write-Verbose, Write-Output / implicit output does not work.

• Capturing the output from this nested pipeline in a variable or sending it through the pipeline requires enclosing the method call in (...) (or $(...) or @(...)) in addition to applying the appropriate redirection to the success output stream (e.g., 4>&1 for the verbose stream).

See the code comments for details.

Add-Type -TypeDefinition @'
  using System.Management.Automation;

  public class Write
  {

      public static void Verbose(string msg)
      {
        using (PowerShell ps = PowerShell.Create(RunspaceMode.CurrentRunspace)) {
          // IMPORTANT: Use .AddScript(), not .AddCommand().
          //            Even though .AddCommand() + .AddParameter() is arguably a cleaner way to
          //            formulate the command, it results in output that cannot be captured.
          //            As noted, Write-Output / success-stream output does NOT work.
          ps.AddScript("Write-Verbose '" + msg.Replace("'", "''") + "'").Invoke();
        }
      }

  }
'@

#"

$VerbosePreference = 'Continue'
    
# Regular output to the verbose stream.
Write-Verbose 'msg1'

# Verbose output via the custom type.
[Write]::Verbose('msg2')

# SUPPRESSING and REDIRECTING TO A FILE work.
[Write]::Verbose('msg3') 4> $null
[Write]::Verbose('msg4') 4> t.txt

# By default, REDIRECTING TO THE STANDARD OUTPUT STREAM (1) 
# works only for the OUTSIDE, i.e. for CALLERS of this script.
[Write]::Verbose('msg5') 4>&1

# Redirecting to the standard output stream (1) can also be used to:
#  * CAPTURE the result INSIDE your script
#  * SEND THE RESULT THROUGH THE PIPELINE, 
# additionally invoke the method call enclosed in (...) or $(...) or @(...)
$out = ([Write]::Verbose('msg6') 4>&1); "captured: [$out]"
([Write]::Verbose('msg7') 4>&1) | ForEach-Object { "piped: [$_]" }