Rather than trying to use Robocopy to not copy, you can use Powershell to update the timestamps.
To update file or folder modified dates, in Windows, similar to Linux/Unix 'touch' utility, use Powershell's set-itemproperty cmdlet.
Your command would look something like this:
set-itemproperty -path $Yourfile -name lastwritetime -value "2021-05-18 10:17:47"
Use get-childitem
cmdlet to walk the file tree (either one level or add -recurse option to descend the folder/file tree).
Your loop would look something like this:
$filelist = get-childitem C:\Users\You\* -recurse
foreach ($file in $filelist) {
set-itemproperty -path $file -name lastwritetime -value "2021-05-18 10:17:47"
}
There are options associated with Get-ChildItem to grab only files or only folders.
In Powershell window type Get-Help Get-ChildItem or Set-ItemProperty for more options.