What does Microsoft.Security.Application.Encoder.UrlPathEncode do?

You can take a look at the source code

From the source code for the method

/// <summary>
/// URL-encodes the path section of a URL string and returns the encoded string.
/// </summary>
/// <param name="input">The text to URL path encode</param>
/// <returns>The URL path encoded text.</returns>
[System.Diagnostics.CodeAnalysis.SuppressMessage(
    "Microsoft.Design",
    "CA1055:UriReturnValuesShouldNotBeStrings",
    Justification = "This does not return a full URL so the return type can be a string.")]
public static string UrlPathEncode(string input)
{
    if (string.IsNullOrEmpty(input)) 
    { 
        return input; 
    } 

    // DevDiv #211105: We should make the UrlPathEncode method encode only the path portion of URLs. 
    string schemeAndAuthority; 
    string path; 
    string queryAndFragment; 
    bool validUrl = UriUtil.TrySplitUriForPathEncode(input, out schemeAndAuthority, out path, out queryAndFragment);

    if (!validUrl) 
    { 
        // treat as a relative URL, so we might still need to chop off the query / fragment components 
        schemeAndAuthority = null; 
        UriUtil.ExtractQueryAndFragment(input, out path, out queryAndFragment); 
    } 

    return schemeAndAuthority + HtmlParameterEncoder.UrlPathEncode(path, Encoding.UTF8) + queryAndFragment; 
}

You will have to dig deeper to get to all the moving parts in encoding the uri. Usually I would recommend looking into the unit tests to see what is expected of the component but there is no tests on the Encoder class at first glance :(