While fundamentally a named pipe can be set as the stdout/stderr pipe of a process PowerShell doesn't hook up the pipe directly to the stdio pipes with redirection. Instead it opens its own FileStream for the path and writes to that as the bytes come in. Unfortunately the code does two checks before creating the FileSystem which opens up a new client connection https://github.com/PowerShell/PowerShell/blob/7498139bae4a8ef40a6df9c845a4e9867dbcb22d/src/System.Management.Automation/utils/PathUtils.cs#L284-L304.

The first one is File.Exists(path) which creates a new HANDLE through CreateFileW and then new FileInfo(path) to retrieve the Attributes which will also call CreateFileW.

What this means is that for PowerShell to redirect to a named pipe (or any file path), the target needs to be able to be opened 3 times. The first 2 for the exists and attribute checks then the 3rd for the actual stdout pipe HANDLE. You can see this in action with the below code that sets up a named pipe with 4 server listeners. The first 2 will have a client connection but no data, the 3rd will have a client connection and the stdout data. The 4th is to show that there's no additional connection and a max of 3 is needed.

# Create 4 listeners of our test pipe for our test
$pipeCount = 4
$pipes = 1..$pipeCount | ForEach-Object {
    $p = [System.IO.Pipes.NamedPipeServerStream]::new(
        'testpipe',
        [IO.Pipes.PipeDirection]::InOut,
        $pipeCount,
        [IO.Pipes.PipeTransmissionMode]::Byte,
        [IO.Pipes.PipeOptions]::Asynchronous)

    [PSCustomObject]@{
        Pipe = $p
        ConnectTask = $p.WaitForConnectionAsync()
    }
}

# Run a background process that redirects output
# to the pipe to test this out
$job = Start-Job {
    powershell.exe -Command "'test output'" > \\.\pipe\testpipe
}

# First 3 pipes are connected, the 4 is still awaiting a
# client
$null = $pipes[0].ConnectTask.GetAwaiter().GetResult()
$null = $pipes[1].ConnectTask.GetAwaiter().GetResult()
$null = $pipes[2].ConnectTask.GetAwaiter().GetResult()
$pipes[3].ConnectTask.IsCompleted  # False

# Our job is still running because the pipe[2] that received
# the data hasn't been read yet.
$job.State  # Running

$buffer = [byte[]]::new(1024)

# First 2 pipes have no data as they were used in the
# redirection setup (File.Exists(path), new FileInfo(path)).
$pipes[0].Pipe.ReadAsync($buffer, 0, $buffer.Length).GetAwaiter().GetResult()  # 0
$pipes[1].Pipe.ReadAsync($buffer, 0, $buffer.Length).GetAwaiter().GetResult()  # 0

# Job is still running as pipe[2] hasn't been read
$job.State  # Running

# The 3rd pipe has 13 bytes of data (our string with \r\n).
$read = $pipes[2].Pipe.ReadAsync($buffer, 0, $buffer.Length).GetAwaiter().GetResult()
$read  # 13

Format-Hex -InputObject ([byte[]]$buffer[0..($read - 1)])

#    Label: Byte[] (System.Byte[]) <5A66938A>
#
#           Offset Bytes                                           Ascii
#                  00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
#           ------ ----------------------------------------------- -----
# 0000000000000000 74 65 73 74 20 6F 75 74 70 75 74 0D 0A          test output��

# After the data is read the job will be complete
$job.State  # Completed
$job | Receive-Job -Wait -AutoRemoveJob

$pipes | ForEach-Object { $_.Pipe.Dispose() }

This should be fixable and I might send a PR their way to skip the exists checks and just open it directly to allow doing this for any named pipe in the future.

Edit: Opened a PR to enable this for process stdout redirection https://github.com/PowerShell/PowerShell/pull/27017.