You can also use UI Automation to close Edge window.

'* Add a Reference to the UIAutomationClient Library(UIAutomationCore.dll)
Public Sub CloseEdgeWindow()
  Dim uiAuto As CUIAutomation
  Set uiAuto = New CUIAutomation
  Dim elmRoot As IUIAutomationElement
  Set elmRoot = uiAuto.GetRootElement
  Dim cndChromeWidgetWindows As IUIAutomationCondition
  Set cndChromeWidgetWindows = uiAuto.CreatePropertyCondition( _
        UIA_ClassNamePropertyId, _
        "Chrome_WidgetWin_1" _
  Dim aryChromeWidgetWindows As IUIAutomationElementArray
  Set aryChromeWidgetWindows = elmRoot.FindAll(TreeScope_Children, cndChromeWidgetWindows)
  Dim wptn As IUIAutomationWindowPattern, i As Integer
  For i = 0 To aryChromeWidgetWindows.Length - 1
    If aryChromeWidgetWindows.GetElement(i).CurrentName Like "*- Microsoft" & ChrW(&H200B) & " Edge" Then
      Set wptn = aryChromeWidgetWindows.GetElement(i).GetCurrentPattern(UIA_WindowPatternId)
      wptn.Close
    End If
End Sub
											
So happy to let me know. This code is what I want to know and surely works. Great and thanks so much! I am going to follow the coding and apply other cases. Thanks again, Kinuasa-san.  
If you could imagine how to translate VBA for IE coding below into VBA for Edge, please give me hints. I still cannot find the key vba code which is for IE and which is for Edge.   
(Start)  
Dim objIE As Object  

Dim sh As Object  

Dim win As Object  

Dim document_title As String  
Set sh = CreateObject("Shell.Application")  

For Each win In sh.Windows  

On Error Resume Next  

document_title = ""  

document_title = win.document.Title  

On Error GoTo 0  
If InStr(document_title, "murai") > 0 Then  

Set objIE = win  

Exit For  
End If  

(FIn)
											
Microsoft Edge is not support the COM automation like IE.    

For automation scenarios, you can use the WebDriver.    
 https://learn.microsoft.com/en-us/microsoft-edge/webdriver-chromium/    
 https://stackoverflow.com/questions/69118936/vba-script-to-convert-from-internet-explorer-to-edge-or-chrome-browser    
											
Yes, as you mentioned, the WebDriver like Selenium Basic could be fine if install is allowed. Many PC controlled under company unfortunately are not around me, at least though.  

So, I am looking for VBA that directly codes on Edge or Chrome browser.   

The translation tool from for IE into Edge or Chrome would be great but still I cannot find it.  
kinuasa-san's code to close edge window is great for me. Thank to it, a VBA I used via IE was able to convert them via Edge smoothly. I don't imagine that just one line code is fine in IE. But still just only one VBA I ever code is converted.  
Anyway thanks your hints, thanks your time, thanks your advise. 
			 
Here are a few hints:  

You can get the Window handle of an application using FindWindow API. You may want to use WinSpy or Spy++ to find out what the window class name is.  

You can close a window by using PostMessage API to send it a WM_CLOSE message.  
With the above keywords you should be able to do your own research and put the code together.  

For the API declarations this is a good reference: https://www.microsoft.com/en-us/download/details.aspx?id=9970  
											
Yes, PostMessage  + WM_CLOSE is the right method (I tested on my version, Edge just doesn't restore previously opened tabs when it is re-started)  

The only problem is that the class is "Chrome_WidgetWin_1" and other apps can have this class, at least "Google Chrome"  

So he should use APIs like EnumWindows to check the class name then get the .exe from the PID (from GetWindowThreadProcessId ))  
			 
kinuasa-san
Your advise was great. So I make use of your code (cf: following).  

But I have 2 questions.
  When Edge doesn't have any tabs, "aryChromeWidgetWindows.Length" seems not to detect Edge so that "aryChromeWidgetWindows.GetElement(i).CurrentName" can't get "Edge's caption".  

    As a result, Edge isn't closed.
  If Edge has some tabs, how to close the designated web site.
〔Due to my company's policy, I'd like to solve this matter without installing other software like "Selenium Basic".〕
I would be happy if you could post advise more.
(↓↓Cf. I'm making code.↓↓)
Sub test()
Dim BrWsr As Variant
Dim uiAuto As CUIAutomation  

Set uiAuto = New CUIAutomation
Dim elmRoot As IUIAutomationElement  

Set elmRoot = uiAuto.GetRootElement
Dim cndChromeWidgetWindows As IUIAutomationCondition  

Set cndChromeWidgetWindows = uiAuto.CreatePropertyCondition( _  

UIA_ClassNamePropertyId, _  

"Chrome_WidgetWin_1" _  

Dim aryChromeWidgetWindows As IUIAutomationElementArray  

Set aryChromeWidgetWindows = elmRoot.FindAll(TreeScope_Children, cndChromeWidgetWindows)
Dim wptn As IUIAutomationWindowPattern, i As Integer
    Set BrWsr = CreateObject("Shell.Application")
    TEST_site = "https://www.yahoo.co.jp/"
    Url = "microsoft-edge:" & TEST_site
    BrWsr.ShellExecute Url
        For i = 0 To aryChromeWidgetWindows.Length - 1
             If aryChromeWidgetWindows.GetElement(i).CurrentName Like "*- Microsoft" & ChrW(&H200B) & " Edge" Then
               Set wptn = aryChromeWidgetWindows.GetElement(i).GetCurrentPattern(UIA_WindowPatternId)
               wptn.Close
             End If
End Sub
When Edge doesn't have any tabs, "aryChromeWidgetWindows.Length" seems not to detect Edge so that "aryChromeWidgetWindows.GetElement(i).CurrentName" can't get "Edge's caption".  

As a result, Edge isn't closed.  
タブが無い状態というのが分からないのですが、一つの方法として、  
 表示されているウィンドウからプロセスIDを取得  
 取得したプロセスIDからプロセス名を取得  
 プロセス名が「msedge.exe」である場合に処理を行う  
といった方法が考えられます。  
If Edge has some tabs, how to close the designated web site.  
ページのタイトルを指定してEdgeのタブを閉じる方法が考えられます。  

プロセスIDからEdgeのウィンドウを判別して処理する方法とまとめると下記のようなコードです。  
https://gist.github.com/kinuasa/c28b76bc60122b1a2cd2ba63c5459796  
なお、私が上で挙げたコードはUIに依存するものです。  

バージョンアップに伴いEdgeのUI、ウィンドウ構造が変更された場合は動作しなくなるような、安定性に欠けるコードになりますので、プログラムによってEdgeを操作する場合は本来的には公式に用意されているWebDriver(Selenium)等の手段を使用された方が良いだろうと思います。  
更に、コードも作成して下さり大感謝です。  

短期間にここまでして下さり、頭が下がります。  

コードを一見しただけですが、こんなにボリュームのあるコードでないと指定のタブを閉じられないのですね。。。自力では到底無理でした。  

kinuasa様のアドバイスを元に取り組んでみようと思います。  

Thanks for your advise so much.  

Furthermore you made a code which solved my question for short time. I admire you.  

I'll try to solve these matters based on your advise again.