What does it mean When people say employers and authorities look at the digital footprint

So I know the basic idea that my digital footprint is my web presence but I don’t get how much information add companys, employers and the government (I’m uk) will be able /can see.
Can they see:
My dms
websites search history
-accounts that do not have my real name attached
-accounts that do not have an email with my name attached eg signed up with fakename@emailadress.com instead of Johnsmith@emailadress.com

If they can see this will it cause issue if …

accounts basic can digital digital footprint dms don employers government history idea information people presence privacy search web websites