Mac mini and iMac display

Nope, the newer Mac’s do not support Target Display Mode.

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

If you choose a Mac mini, then you will also need an external display.

see > Connect a display to Mac mini - Apple Support

That iMac doesn't support Target Display Mode, period.

According to MacTracker, model identifier "iMac18,2" corresponds to an iMac (Retina 4K, 21.5-inch, 2017). Target Display Mode went away when the first Retina iMac came out in Late 2014. No Retina iMacs have it.

mc72scott wrote:

With every update it gets slower.

Unless you're running an unusually demanding workload, the amount of memory you have (32 GB) isn't the issue. The CPU isn't a barnburner by current standards, but I doubt if it responsible for it taking 2 or 3 minutes to open a Safari window (once the computer is up and running), either.

I suspect that you have some software running on that machine that is causing it to bog down. Maybe an anti-virus application (that's constantly doing work in the background), or a "cleaner" application, or something like that.

Another reason the machine may be slow is the internal drive. That iMac came with

• A 1 TB mechanical hard drive (2.5"-type, 5400 rpm),
• A 1 TB Fusion Drive with the same slow mechanical hard drive, and a measly 32 GB of SSD storage, or
• 256 GB - 1 TB of flash (SSD) storage

If you are starting up off a 1 TB hard drive or 1 TB Fusion Drive, you might benefit from getting an external SSD, and using it as your startup drive. That iMac has modern expansion ports – USB-C (Thunderbolt 3) and USB-A (USB 3) – that would let you use a wide range of modern SSDs.

But the report of 2 or 3 minute times to open a Safari window on a machine with 32 GB of RAM makes me think that something other than "just" a slow mechanical drive or Fusion Drive is the culprit. Maybe software which you could remove; maybe a failing internal hard drive (which could be a harder problem to solve).