How can WIX create a website in IIS in parallel to the default web site (this is directly under sites)

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IIS10

Hello,

I need to place our WebSite under Site in IIS using WIX.
(I use a WIX Setup-Project in VS2022 -> I create a msi-file.)

Like so:

SomeServer
|->Application Pool
|->Sites
..|->Default Web Site
..|->My New Web Site <- this is what I want.
A new website under Sites, not under the Default Web Site.

What I have tried:

I followed this great article:
https://www.codeproject.com/Articles/115036/Creating-WIX-Installer-for-ASP-NET-Web-Application

I think the important part in the article is:

<?xml version="1.0" encoding="UTF-8"?>
<Wix xmlns="http://schemas.microsoft.com/wix/2006/wi"
     xmlns:iis="http://schemas.microsoft.com/wix/IIsExtension"
     xmlns:util="http://schemas.microsoft.com/wix/UtilExtension">
    
    <Fragment>
        <?include ConfigurationInitialize.wxi ?>

        <!-- Install to default web site -->
        <iis:WebSite Id="DefaultWebSite" Description='Default Web Site'>
            <iis:WebAddress Id="AllUnassigned" Port="80" />
        </iis:WebSite>

        <DirectoryRef Id="MYWEBWEBSITE">
            <!-- Configuring app pool -->
            <Component Id="MyWebAppPoolCmp" Guid="" KeyPath="yes">
                <util:User Id="MyWebAppPoolUser"
                           CreateUser="no"
                           Name="[WEB_APP_POOL_IDENTITY_NAME]"
                           Password="[WEB_APP_POOL_IDENTITY_PWD]"
                           Domain="[WEB_APP_POOL_IDENTITY_DOMAIN]" />
                <iis:WebAppPool Id="MyWebAppPool"
                                Name="[WEB_APP_NAME]"
                                Identity="other"
                                User="MyWebAppPoolUser" />
            </Component>
        
            <!-- Configure virtual dir -->
            <Component Id="MyWebVirtualDirCmp" 
                   Guid="{751DEB01-ECC1-48ff-869A-65BCEE9E0528}" 
                   KeyPath="yes" >
                <iis:WebVirtualDir Id="MyWebVirtualDir" 
                          Alias="[VIRTUAL_DIR_VAL]" Directory="MYWEBWEBSITE" 
                          WebSite="DefaultWebSite">
                    <iis:WebDirProperties Id="MyWebVirtDirProperties" 
                       AnonymousAccess="no" BasicAuthentication="no" 
                       WindowsAuthentication="yes" />
                    <iis:WebApplication Id="MyWebWebApplication" 
                       Name="[VIRTUAL_DIR_VAL]" />
                </iis:WebVirtualDir>
            </Component>
        </DirectoryRef>

        <ComponentGroup Id="MyWebIssConfiguration">
            <ComponentRef Id="MyWebVirtualDirCmp" />
            <ComponentRef Id="MyWebAppPoolCmp" />
        </ComponentGroup>
        
    </Fragment>
</Wix>

But that puts the new WebSite under the Default Web Site:

SomeServer(xxx\myName)
|->Application Pool
|->Sites
..|->Default Web Site
....|->My New Web Site <- this is not what I want.
New Web Site is under the Default Web Site