To answer your questions, no, and no...
A Recreational certificate is issued to the pilot, not to the aircraft.
If you signed up for a Recreational certificate in the USA, YOU have one registration number – yours – which goes on each and every recreational aircraft you own. It doesn’t matter if you have 1 or 20 drones, that number goes on every one of them.
You paid one registration fee to register yourself, not a drone. That number can be used on all your hobbyist drones.
You do not need to cancel that aircraft’s registration as a Recreational aircraft; in fact the aircraft isn’t registered, you are!
(On the FAA Drone Zone website there is no way to manage a recreational aircraft inventory, but there IS on the Part 107 side...and an aircraft displaying a Part 107 registration number may also be used for recreational purposes.)
If however you have an aircraft that will be used in part 107 operations you must register each individual aircraft which will be issued a unique registration number. If you have 20 drones you’ll wind up paying 20 individual fees and will get 20 unique aircraft registration numbers.
In Part 107 operations YOU must have a Part 107 pilot certificate; in addition to that EACH aircraft must be individually registered and have a unique registration number.
If you have an aircraft that currently is labeled with your Recreational pilot certificate number, and you wish to use that aircraft for Part 107 operations, register the aircraft under Part 107 and put that (P107)registration number on the aircraft. Remove your Recreational pilot certificate number from the aircraft.
So go out and fly your aircraft that you registered under Part 107 with its unique number, and make sure you take your temporary authorization as a Commercial Remote Pilot with you and you’ll be fine.
I have asked this question of the FAA before, and that was their answer.
And by the way, one reason you should likely stay registered as a Recreational pilot as well as a Commercial one is if you buy another drone and you’re not sure if you want to use it in commercial service. You could always put your recreational number on it to fly out for testing, training and evaluation or just for fun.
In this way you don’t have to go and individually register (and pay a fee) for every drone you own as a Part 107 bird - just the ones you’ve decided you want to use for commercial purposes.