Will Mac Mini with M2 connect to my Apple iMac (late 2015) running OS 10.13.6 to use as a workable monitor

No. Only a few iMac models prior to mid-2014 could ever be used in target display mode. And they will not work with any post-2019 model Mac (mini or otherwise).

Details here -> Use your iMac as a display with target display mode - Apple Support

+1 Nope. Please refer to Target Display Mode, if you need an external display please buy one. You will find this is more reliable, has simple setup, does not require expensive cabling and will fit just about every budget.

That iMac doesn't support Target Display Mode. Apple dropped that feature back in Late 2014 when the first 27" 5K Retina iMac came out.