Magic Mouse A1296/Keyboard A1314 with M4 iMac/Mac mini
Are Magic Mouse Model A1296 3Vcd (Year 2013) and Bluetooth Keyboard Model A1314 (Year 2009) compatible with iMac M4 and Mac Mini M4?
Short answer: no. Neither would be suitable.
As far as the A1314 keyboard (aka, Apple Wireless Keyboard,) it came out in 2009 and was designed to work with macOS Ventura and Sonoma, but may experience occasional connection issues on newer systems due to it is limited to Bluetooth 2.0.
For the Magic Mouse, the A1296 is a 1st generation Magic Mouse that also came out in 2009. It was designed to work with OS X Leopard / OS X Snow Leopard.