There could be 2 different cases with different results.
When hackers offer you to pay for a fabricated invoice and send you a link to a legit payment system (e.g. PayPal) which contains invoice, only your money are at risk. In this case, crooks just try to make you pay for a thing you should not to. Once such a payment has failed, you are not losing anything. But I’d recommend you to block the sender and delete the message anyways.
The other situation involves a fake payment system page. It is relatively easy to make a copy of a legit payment system, and then make the victim visiting it “to pay off the bill”. Same as in the first case, bill is non-existent, but this time hackers also put their hands on your credit card info. As this copy is made and maintained by hackers, there’s no problem for them to extract what did you type in the fields on the site. If that is the case, you should reach your bank and ask to block and re-issue the card, so the info hackers have collected through such a phishing will be useless.

Hello, Leslie!
Even having your address/personal number or similar “less critical” personal information, threat actors can impersonate you. Alternatively, you may start receiving numerous spam SMS. They will not be targeted, as crooks who phish such data usually sell it off in bundles to other rascals, but still unpleasant and annoying. And the more data crooks have – the higher are chances to receive a very convincing phishing mail, which will be extremely hard to distinguish from a legit one.