If we use the standard allowance for revenue loss and spend ARPA funds on public health & economic response, premium pay, or water, sewer and broadband, should I still report them under the Expenditure Category 6.1?

Yes, report ALL spending under Expenditure Category 6.1 Provision of Government Services, regardless of the type of project you undertake or spending using your ARPA award.

Source: Treasury 3/21 webinar: https://youtu.be/0NE1ZQXzOWo (minute: 13:55)