Your payroll information is sent to the Tax Office each week, and your electoral enrolment and plenty of other government agencies have your address, so they know where you are the vast majority of the time. It's just pulling together multiple data points that they already have.No they can't. They don't have access to my movements unless I give it to them.
They might have access to yours if you carry your smart phone everywhere you go. To make this work practically that would become mandatory.
I also don't think the vaccine passport works in the way you are suggesting. My understanding it is a bit like using your drivers license or other ID to get into licensed premises (back before I went grey and bald) - you just show it upon entry and that's that.