Magic Mouse compatibility with Late 2013 iMac

Currently using an old 'Magic Mouse' Version 1, Model No: A1296 (the one with AA Batteries) which has started to 'lose connection' with my late 2013 27 inch iMac which is running macOS Catalina Version 10.15.7.

Purchased a new 'Magic Mouse', Model No: A1657, with a view of replacing my current old Magic Mouse (A1296) as the specifications say it will work with OS X 10.11 or later which my iMac is - Version 10.15.7.

Problem!

New Magic Mouse (A1657) comes with USB-C to Lightening Cable. My late 2013 iMac only has USB-A ports. To pair the new 'Magic Mouse' the supplied instructions say the following:

"To pair your mouse with your Mac, use the USB-C to Lightening Cable that came with your mouse. Plug the Lightening end into the Lightening port on the bottom of your mouse. Plug the USB-C end into a USB-C port on your Mac. Slide the on/off switch to on (so green is visible). Your mouse will pair automatically with your Mac. After the mouse is paired, disconnect the cable to use your mouse wirelessly".

So at this stage I'm unable to pair the new Magic Mouse to my iMac as previously mentioned my iMac only has USB-A ports UNLESS I now go and purchase a USB-A Cable with USB-C connector.

Has anyone else had this problem?

Am I correct in saying that I now need an additional cable to get the new mouse 'paired' with my late 2013 27 inch iMac?