Yes, the micro:bit processor in the Hummingbird Bit and Finch Robot 2 is the standard micro:bit that you find elsewhere, so you can use your existing micro:bit with either product. The Finch Robot 2 and Hummingbird Bit are compatible with both micro:bit V1 and micro:bit V2.
Both the Hummingbird Bit and the Finch Robot 2 do require a micro:bit to work, so if you do not already own a micro:bit you should purchase one with your robot.
The power behind the BirdBrain tools + micro:bit connection is that you get two learning tools combined into one! You can use the micro:bit to do separate projects that you would find on their website, but you are also able to take your learning to the next level by adding external components and multiple programming languages with the BirdBrain robots.