Use new M2 to drive old iMac display

According to MacTracker, iMac14,4 is an 21.5" mid-2014 iMac. Even if the M2-based Mac supported using an iMac with TDM as a second display,, you'd need $80 in Thunderbolt connection hardware (a $50 TB3-to-2 adapter, plus a $30 TB1/2 cable) to reuse a 9-year-old, 21.5" 1920x1080 screen.

It wouldn't make a whole lot of sense, given the prices of real 24" 1920x1080 monitors – ones which would be more convenient to use. I believe that you can even get some decent 27" 4K monitors for $300 – $350 if you look around a bit.

But no M2 Mac supports using any iMac as a TDM display. The M2 Macs are too new to satisfy the restrictions that Apple placed on "the other Mac."

Nope' the new iMac does not support using the old 2012 iMac as a display in Target Display Mode.

carefully read > Use your iMac as a display with target display mode - Apple Support

You can't if you are referring to a Mac mini or Studio.

The keyboard is another matter. If you won't be using the 21.5" iMac any more, you may be able to transfer that to the new M2 system.