RE: "Am I running a OS that is too advanced for my iMac?"
I'm sure that Monterey loves RAM and fast startup disks. So let's do a quick review:
iMac (Retina 5K, 27-inch, Late 2015) - Technical Specifications
That machine would have shipped with at least 8 GB of RAM. Since it is a 27" iMac, the RAM is user-upgradable. The official limit is 32 GB, but the actual limit is 64 GB (as per MacTracker, Other World Computing, and Crucial).
If you think you don't have enough memory, you might want to use the Memory Pressure graph in Activity Monitor (while doing the things you normally do) to see if it shows yellows and/or reds. But even if you have 8 GB of RAM now, that's enough that a simple Finder search in Monterey should not be causing the hangs you report. Looks to me like something is going on other than a "not enough RAM" problem.
The machine would have shipped with one of these drives:
- a 1 or 3 TB 7200rpm SATA HDD,
- a 1, 2, or 3 TB Fusion Drive, or
- 256 GB, 512 GB, or 1 TB of flash storage
If your drive is a pure hard drive, an external USB 3 SSD startup drive would definitely help you with overall performance. If it is a 1 TB Fusion Drive, I also think an external USB 3 SSD startup drive might be in order. (The 1 TB Fusion Drives for this model year included only a miserly 24 GB of flash storage.)
If you're lucky enough to have flash storage, it's faster than anything you could attach to the USB 3 ports. As for a 2 TB or 3 TB Fusion Drive, those included 128 GB of flash storage, which might be enough for their performance to hold up well even under Monterey.