How to access properties in a nested hashtable without explicitly stating the property names?

Let's say I have a 2-level nested hashtable like this:

$programs = @{


    program1 = @{
        DisplayName = "DisplayName1"
        Program = "C:\program1.exe"

    }

    program2 = @{
        DisplayName = "DisplayName2"
        Program = "C:\program2.exe"

    }

    }

now, without explicitly mentioning each of the property names like this:

$programs.program1['program']

I want to iterate over the hashtable like this:

foreach ($Name in $programs) {


$r = Get-NetFirewallRule -DisplayName $programs.Keys['DisplayName'] 2> $null; 
if (-NOT $r) { 
                         
New-NetFirewallRule -DisplayName $programs.Keys['DisplayName']  -Program $program.Keys['Program']
         
}

}

but I keep getting errors like:

 Cannot validate argument on parameter 'DisplayName'. The argument is null. Provide a valid value for the argument, and then try running the command again.
InvalidOperation: untitled:Untitled-2:29:13

what am I doing wrong?

what is the right way to access nested hashtable properties like this without explicitly mentioning their names? I want to know the synatx of it so that if I ever have a 3 or 4 level nested hashtables I can access them without specifying their exact names.

even if we ignore the foreach loop, how to only list all the "DisplayName" properties? what if the "DisplayName" properties were in a 4-level nested hashtable and we wanted to list them in the PowerShell console without specifying the exact names of the items that came before it?

Thanks to the comments from Santiago Squarzon and zett42, here is the syntax to access properties of deeply nested hashtables.

$programs.Values.Values.Values and so on.

I found it work perfectly.

also, after reading foreach and as mentioned in the comments, I found that my code above was incorrect and the correct way is this:

foreach ($Name in $programs.values.GetEnumerator()) {


$r = Get-NetFirewallRule -DisplayName $Name.DisplayName 2> $null; 
if (-NOT $r) { 
                         
New-NetFirewallRule -DisplayName $Name.DisplayName -Program $Name.Program
         
}

}

in a foreach loop, we have to use the variable we create in the parenthesis. my mistake was that I was using the collection itself again.