Big Sur doesn't recognize my printer

Did you make a clone backup before upgrading? Clone back your system you backed up from, after booting it.

If you made a Time Machine backup that you haven't access, you can recover after erase and installing Mojave. To erase and install Mojave:

1. command-option-shift-R at startup. Use Disk Utility to format the top most partition of show all partitions.

Run the installer to install the system. Note, if the system it came with is Sierra or older, you'll need to format the partition as

Mac OS Extended Journaled

Before running the installer, as Sierra, El Capitan, Yosemite, Mavericks, Mountain Lion and Lion don't support APFS, High Sierra and Mojave do.

2.If you have install something older than Mojave first, upgrade to Mojave following these directions.

If you didn't back up your system downgrading upgraded applications can be difficult at best, incompatible at worst. Make sure all your documents are saved as their older counterpart versions in a separate folder.

Photos libraries and Music libraries upgraded in the process may no longer be compatible, and playlists and albums may be lost, but the originals can be reimported.

Unfortunately Epson is behind the eight ball.

https://epson.com/Support/Printers/All-In-Ones/WorkForce-Series/Epson-WorkForce-WF-3640/s/SPT_C11CD16201

shows no compatibility for Catalina, let alone Big Sur.

You might be able to use the built-in open source drivers, using the Option key when selecting the + sign on Apple menu -> System Preferences -> Printers to add the printer.

If it still fails to see it, it is best to get a printer with known compatible drivers for Big Sur.

https://discussions.apple.com/docs/DOC-250003076

Or downgrade your system if it is older than Catalina (October 2019).

https://discussions.apple.com/docs/DOC-1948

Drivers are available. Quote on support page:

"Attention macOS 11 Big Sur users: Your new operating system may not be detected correctly below. While we work to resolve this, it's important that you manually select "macOS 11.x" in the Operating System drop-down menu below to ensure you're viewing only compatible files."

https://epson.com/Support/Printers/All-In-Ones/WorkForce-Series/Epson-WorkForce-WF-3640/s/SPT_C11CD16201?review-filter=macOS+11.x#drivers

Yes.