Hello there. Any cancellation initiated by you and accepted by a (new or old) buyer or initiated by a buyer and accepted by you, will decrease your completion rate. If that rate drops below 90% and is below 90% still on level evaluation day, you’ll also get demoted from level 2 to level 1 (which may or may not be an issue, as buyers sometimes do say they thought level 1 is the better of the two…). With a completion rate of under 90%, you also can’t send offers to buyer requests.
If the buyer insists on you doing work that your gig clearly does not cover, if your gigs are clear on what you offer for which price, I would ask support to cancel the order for you on the grounds that the buyer bought the cheapest gig instead of the one that matches what he wants done and refused to pay more even though you explained.
There is no guarantee that the cancellation done by support won’t count, but the only chance. If you cancel yourself, it will definitely lower your rate.
You could try reaching an olive branch to your buyer first, though, explain in a super nice way that they must have accidentally chosen the wrong gig for the work they want you to do, etc. and offer again to upgrade the gig they bought to the gig they actually need. Either it works, or if not, you can right away tell support you already tried twice, so they won’t tell you to work it out with the buyer, which will only waste buyer’s and your time if they really don’t want to pay the appropriate amount.
I don’t interpret the new “This is a new buyer, please make their experience a great one” bit as doing work for free or let ourselves be bullied by buyers but to help them understand how Fiverr works if needed, to be nice if they have a question or two more than seasoned buyers (and of course all the stuff you do anyway, no matter if new or old buyer, like be polite, deliver on time, communicate when needed, …)
I see it more like a heads-up “Attention, person is new, probably doesn’t know how all this works, there may be issues, technical or otherwise, with them, please stay patient and attentive and explain/help them if it seems like they need it”.