Using iMac as a display.

No.

Review the document: Use your iMac as a display with target display mode - Apple Support

Target display mode is/was a feature available with late 2009-Mid 2014 iMacs. The display Mac has to be running macOS High Sierra or older and the signal producing Mac has to be running macOS Catalina (ca. 2019) or earlier.

This could only be done with a very few and very specific older iMacs and support was very limited. Read this topic for a 2021 perspective on this: Using iMac as an external screen - Apple Community

and this 2021 post by Allan Jones about software limitations:

TDM configuration - Apple Community

and read about Screen sharing Share the screen of another Mac - Apple Support

Related thread with information about Luna Display: iMac as display for M4 Mac mini - Apple Community

+1 No.

As @den.thead already suggested, get a decent external display for use with a Mac mini. Most displays these days have HDMI connections, as does the mini, but the mini also supports connection to displays via Thunderbolt 4, Thunderbolt 5 and DisplayPort 1.4 & 2.1 (adapters may be required).

You could use the iMac with the mini via Screen Sharing but you would still need an external display to set up the mini in the first place. And while screen sharing works surprisingly well it's nowhere near the same as having a real display connected directly to the mini. I do not suggest Screen Sharing as a substitute for a real display.

Target Display Mode went away when the first 27" 5K Retina iMac came out in Late 2014. It never came back, so your 27" 5K Retina iMac, from the following year, doesn't have it, either.

+1 No.

If you are considering an M4 Mac mini, also plan on getting a decent after-market external display.

see > Connect a display to Mac mini - Apple Support

davidb2119 wrote:

Would the migration assistant work to help the changeover?

I am assuming that is a separate and unrelated question. To learn how to use Migration Assistant please read Transfer to a new Mac with Migration Assistant - Apple Support. Wireless is easiest so try it first.