Alright. Changing the encoding to UTF8 fixed the issue.

I am glad it seems to be working for you now.

A couple of points:

1. The encoding shown on Notepad++'s status line is an estimate based on inspecting the file. The inspection process is not perfect and so I would not load a file into Notepad++ and 100% rely on what it says the encoding of that file seems to be. I have had Notepad++ say “ANSI” for example even when the file has 3 or 4 byte long UTF-8 encoded sequences near the beginning. Figuring out the encoding of a file can be a long topic in itself.
2. In your code I’m bothered by your use of -NoNewline -Encoding OEM. It just seems weird and is the sort of thing that will lead to unexpected results down the road. However, this forum is about Notepad++ and so I’ll leave it at that rather than topic-drifting into encoding and PowerShell.

Alright. Changing the encoding to UTF8 fixed the issue. Below is the full solution:

$path = "c:\Users\$($env:username)\Documents\Workspace File" 
(Get-Content $path) -replace "username1","username2" | out-file $path 
Set-Content -NoNewline -Encoding OEM $path -Value (Get-Content -Raw -Encoding utf8 $path)

Or alternatively, with arguments:

$replace1 = args[0]
$replace2 = args[1]
$path = $args[2]
$encoding = $args[3]

(Get-Content $path) -replace $replace1,$replace2 | out-file $path
Set-Content -NoNewline -Encoding OEM $path -Value (Get-Content -Raw -Encoding $encoding $path)

I receive this error when trying to load it in the Project Pane in Notepad++

What do you mean by “workspace file” and “no longer works”?
You see a different content when you open the file with npp? If so, what is different?