Paypal has charged invoicing fees for a long time. It's not a flat 2% either; the invoicing fee is $0.30 plus 1.9% to 2.9% of the amount received.
It's really not worth sending a Paypal invoice. If you are an infrequent seller, just wait for the buyer to pay.
If you are a high volume seller, a freelancer or small business owner and you accept Paypal, you really should be using Freshbooks or Harvest as your online invoicing system and select the Paypal Business Payment option. Doing so avoids the invoicing fee and the 3% surcharge; instead , you pay a flat fee of $0.50 for 'Paypal Business Payments.'
Obviously there's a cost for this. Freshbooks currently charges $19.95/month for up to 25 active or archived customers that you invoice through Freshbooks. Deleted customers don't count towards that 25 total.