I have an older MacBook Pro running OS Catalina. It is not capable of running Big Sur. I want to buy a new MacBook Pro and transfer my files from the old machine to the new, which will come with OS Big Sur. Is that possible?

Yes. See information in: Move your content to a new Mac - Apple Support

Yes. When you get the new computer, begin the steps of setting it up. At one point you will be asked if you wish to import/transfer data from another computer. Answer yes and then connect the two computers with a USB cable and open Migration Assistant to do the transfer. Do not use Wi-Fi. It is too slow and can cause corruption. M.A. is designed for this purpose and does it well. Follow the instructions and answer the few questions you are asked. Your old operating system will not be transferred to the new computer. You will have the option of transferring your apps or reinstalling them. Either way, some will have to be reregistered to activate them in the new computer. Enjoy your new Mac.