PowerShell: Cannot have local variables scoped inside a class method?

I expect that inside a class method, I can have "local" variable scoped inside of the method, but it is not the case. The following is the test code:

class test_scope {
  $var = "class var"

  test_scope() {
  }

  [void] my_method() {
    $var = "method var"
  }
}

$obj = [test_scope]::new()
$obj.my_method()

I got an error message:

Line |
   8 |      $var = "method var"
     |      ~~~~
     | Cannot assign property, use '$this.var'.

This is surprising. How can I have local variables?

As a comparison, function (outside of a class, that is) can have local variables with the same name as the script variable. The following is an example:

$var2="global var"
function my_function() {
  $var2="function var"
  write-host $var2
  write-host $script:var2
}
my_function($null)

and I got the answer I expected:

function var
global var

As another comparison with Python:

class test_scope:
  var = "class var"

  def my_method(self):
    var = "method var"
    print(self.var)
    print(var)

obj = test_scope()
obj.my_method()

It works as expected:

function var
global var

so PowerShell is out of norm?

PS: I tested under PowerShell 5.0 and 7.0.

The accepted answer avoids the problem but doesn't identify its root cause. This is that the scope of a variable must always be specified in class functions, with the exception of parameters that the function receives and class properties. So you can write without any problems:

class test_scope {
    $var = "class var"

    test_scope() {
    }

    [void] my_method() {
        $local:var = "local method var" # or private
        $script:var = "script var"      # or global

        # one can omit local or private scope when reading the variable:
        Write-Host "'$var' vs '$( $this.var )'"

        # one has to use global or script scope also when reading the variable:
        Write-Host "'$( $script:var )' vs '$( $this.var )'" # or global
    }
}

$obj = [test_scope]::new()
$obj.my_method()

Output:

'local method var' vs 'class var'
'script var' vs 'class var'