That date was subject to change---and it changed. The form is not ready for the software yet. You have to wait.
Once the form 1040x is ready and I amend my 2020 return electronically, will I be charged to do this by Intuit? If so, will I be charged for both state and federal amended returns?
No you are not charged for amending your tax return unless whatever you are changing requires an upgrade to a higher version of the software.