This is a complex (and changing) issue. The US and Canada are NOT part of Schengen Area but they currently enjoy some travel benefits under the Schengen Borders Code - essentially you do not need to apply for a travel visa for stays less than 90 days. This is currently set to disappeared in Nov 2023.
The Schengen area allows people in the EU to move freely between Schengen countries, without internal borders. At the same time, the EU and EU countries makes sure that external borders remain protected.
home-affairs.ec.europa.eu
But this has nothing to do with covid requirements. It simply relates to travel visa.
Each country is free to implement any additional security checks seemed necessary. Covid led each country to establish their own covid related entry requirements. So the covid rules within Schengen are inconsistent.