Update all records in a specific report

This can be done with script, but that is coding.
It can be done with a formula URL button and using API_RunImport

But let's see if we can do this with no code.

Make a new table called Payoll Approval.    On that record put a user field (and Make the Key field be a User field),  and a Report Link field and a formula text field called [Link to my Payroll Entries for Approval]

For the [Link to my Payroll Entries for Approval] field make the formula

List("-",UserToName(User()), "Approved")

The effect of that will calculate to John Smith - Approved.

Then on the Payroll records, make a similar formula

List("-", [Manager name userid], "Status")

Use those two fields to configure the Report Link field.

Put the Report Link field on the form for the Payroll Approval and list the records right on the form.

You should see all the records waiting to be Approved for that manager User on the form.

So what we have done is to have created a Report Link field which defines the records to be updated.

Now, make a new checkbox field on the Payroll Approval record.

Now, make an ACTION on the Payroll Approval form that says when the checkbox is checked

EDIT the related records defined by that Report Link and change the value in the field [Status] to the value Approved.

Take a shot at that and we can tidy up the rough edges once you get the ACTION to fire.

Note that when you check the checkbox, you will need to refresh the record  to see the effect.  The effect should be that the report link field goes empty as a report, since there are no longer records waiting  to be Approved.