I need to update my iMac 2013 to Big Sur, what are my options?

If the user whats the latest and greatest versions of macOS,  all is not lost.

Explore the Apple Trade-In  Process where the Value of the exiting device could be used against the cost of a new Apple Computer, iPhone or iPad  

Or Shop Refurbished Apple computers at an Apple Reduced Cost

Have used both previously and have been satisfied each time.

Sorry, but as ghr165 has already mentioned, your Late 2013 iMac is not capable of running macOS Big Sur.

Ref: macOS Big Sur is compatible with these computers - Apple Support

You cannot.