Hello and thanks for the suggestions, @atripp!
I tried doing an Invoke-WebRequest against the repository URL. It appears to work fine, which is nice but also a pain as it indicates the problem is more complicated.
PS C:\> [Net.ServicePointManager]::SecurityProtocol = [Net.SecurityProtocolType]::Tls12
PS C:\> $test = Invoke-WebRequest -UseBasicParsing "https://${progeturl}/nuget/${repository}/"
Invoke-WebRequest: You must log in to issue this request because the anonymous user does not have the Feeds_ViewFeed privilege.
PS C:\>
PS C:\> $test = Invoke-WebRequest -UseBasicParsing "https://${progeturl}/nuget/${repository}/" -Credential $credential
PS C:\> $test
StatusCode : 200
StatusDescription : OK
Content : <?xml version="1.0" encoding="utf-8"?><service xmlns="http://www.w3.org/2007/app"><workspace><title xmlns="http://www.w3.org/2005/Atom">Default</title><collection
href="Packages"><title xmlns="http://…">
RawContent : HTTP/1.1 200 OK
Cache-Control: no-store, must-revalidate, no-cache, max-age=0
Pragma: no-cache
Server: Microsoft-IIS/10.0
X-ProGet-Version: 22.0.7.3
X-Powered-By: ASP.NET
Date: Sat, 24 Sep 2022 …
Headers : {[Cache-Control, System.String[]], [Pragma, System.String[]], [Server, System.String[]], [X-ProGet-Version, System.String[]]…}
Images : {}
InputFields : {}
Links : {}
RawContentLength : 273
RelationLink : {}
PS C:\> echo $test.Content
<?xml version="1.0" encoding="utf-8"?><service xmlns="http://www.w3.org/2007/app"><workspace><title xmlns="http://www.w3.org/2005/Atom">Default</title><collection href="Packages"><title xmlns="http://www.w3.org/2005/Atom">Packages</title></collection></workspace></service>
I will attempt to use a tool like Wireshark or Fiddler to see what's going on.