2015 iMac secondary monitor to mac studio M2

Target Display Mode went away when the first 27" 5K Retina iMac came out in Late 2014. It never returned. Plus, Apple added restrictions on "the other Mac". None of today's Macs support using ANY iMac as a Target Display.

There is a third-party product called Luna Display which might let you use that iMac as a second display. But even if you ran a Thunderbolt connection between the Macs to help support video data transmission, I believe that there would be compromises compared to a hardware connection to a standalone 5K display.

No, iMacs are computers they are NOT external displays for other devices.

Target Display Mode

I agree with Servants of Cat's assessment of Luna. I found this on Luna's support page (screenshot):

That says to me that if all you need is a place to park pallets from other apps, it's fine. However, the US$80 cost would go a long way toward the purchase of a decent external monitor that should not lag at all.