The billing software I use to keep track of my hours/clients/invoices etc. is no longer supported by the manufacturer, and I have to find something else. Is it off-topic here to ask for a suggestion? While it's not strictly about writing, anyone who writes/edits for a living in any capacity does have to keep track of money.
This sounds like a case of boat programming -- in this case, you're asking what's the best way to manage your billing as a writer, but the "as a writer" part isn't actually important to the question. You could ask the same question "as a contract programmer", "as a plumber", "as a private flight instructor", or whatever and you'd get the same answers. So my instinct would be that it's off-topic, quite aside from whether it's a list question.
However, if there are aspects of the question that are specific to writers, a question that focuses on those particular issues could be on-topic.
There is a new SE site specifically for Software Recommendations.
Could be useful.