Upgrading my iMac 2017 w./ MacOS High Sierra (10.13.6)

If I understand you correctly, the Software Update preference says your Mac is up to date? Not so easy then!

Try this link to the App Store: ‎macOS Monterey on the App Store. Be advised that link may only work in the US, so if that's not where you are please let me know.

Well your 2017 iMac will remain slow as it was a base model which was designed for only very minor work such as retrieving e-mail and light web surfing. It is configured with only 8GB of RAM, however the primary bottleneck is the 5400 RPM hard drive. What others in your situation often do is 1 of 2 things.

1. Purchase an external SSD such as a OWC Mercury On-The-Go Pro 1TB SSD Storage Solution and a OWC On the Go Pro Power Adapter and then use a cloning app (either SuperDuper! or Carbon Copy Cloner) to clone their internal HD to the new SSD. Then set the SSD to be their startup drive. This will make performance substantially quicker.
2. The second option is to replace the iMac with a new machine such as a M1 based Mac Mini or M1 based 24" iMac. If you take this option remember to get one with a minimum of 16GB of RAM and the largest capacity SSD you can afford.

Finally, you are not backing up your 2017 iMac, this is a CRITICAL error and a 100% guarantee you will lose important data. If the same holds true for your other Mac you need to begin backing that up too! At the very least you should be using Time Machine ( Back up your Mac with Time Machine ) which only requires and external HD to backup to, many experienced users prefer the OWC Mercury Elite Pro due to it's great build quality, reasonable pricing, great service and ease of servicing. This should be your #1 priority!!!!!!!!!!!

It appears that you do not have a Time Machine backup. If this is the case, you should create one. To start, you need an external hard drive. Here’s a few excellent ones sold by Apple: 

• LaCie Mobile Drive 4TB External Hard Drive USB-C - Apple
• LaCie 4TB Rugged USB-C Portable Hard Drive - Apple

You can then follow the steps in this Apple Support article to setup your Time Machine backup: Back up your Mac with Time Machine - Apple Support. Also, moving forward, I recommend that you use iCloud in addition to Time Machine to sync all your files and photos to all your Apple devices. Although iCloud is not a "true" backup service, iCloud can also act as an emergency off-site backup, but this is why iCloud should be used in addition to Time Machine. Here are some resources on setting up iCloud for Mac:

• Upgrade to iCloud+ - Apple Support
• Set up iCloud Drive - Apple Support
• Add your Desktop and Documents files to iCloud Drive - Apple Support
• Set up and use iCloud Photos - Apple Support

After you setup iCloud, turn off "Optimize Mac Storage" in System Preferences > Apple ID/iCloud. That way, all changes made to files in iCloud are also backed up to Time Machine. If you have this setting on due to a limited amount of storage on your Mac, that is fine. Just know changes won't be backed up to Time Machine, only iCloud.

However, the reason your iMac is slow is due to the 5400-rpm hard drive. While this hard drive found in your Mac is perfectly suited to light tasks, such as email, web browsing, etc., for more advanced tasks, and for users who want the maximum performance from their Mac, this hard drive does have its limitations. Luckily, you can use an external SSD as your startup disk to run macOS and all your data from that. It will make your Mac 10 to 30 times faster for storage, and in turn, make your entire Mac system much faster. For more info, instructions, and what external SSD to buy, please see: How to Setup and Use an External SSD as your Startup Disk on a Desktop Mac - Apple Community.

Jack

Sadly your 2014 MacBook Pro Retina 15 inch is not eligible for Monterey: macOS Monterey is compatible with these computers - Apple Support

So in that case the dialog is correct — the latest current operating system for that Mac is macOS 11.6.2.

It's not unusual for a Mac to perform slowly immediately upon upgrading macOS, but its performance should improve. If you have reason to suspect its performance ought to be better than it is, then by all means start a new Discussion. Before you do that, I recommend that you download and install EtreCheck, then run it and post its report in that Discussion.

Using EtreCheck is harmless and does not affect your Mac in any way; otherwise I would not recommend it. For instructions please read Using EtreCheck - Apple Community. Its report is likely to reveal some actionable information.

Runtime: 165:40

There is slow, and then there is crazy slow. That's crazy slow. I suspect hard disk drive failure will prove to be the cause:

disk0 - APPLE HDD HTS541010A9E632 1.00 TB (Mechanical - 5400 RPM)

Even a Mac with a slow mechanical hard disk drive should not take that long to run EtreCheck.

Diagnosing incipient or intermittent hard disk drive failure is not a trivial task. Although they will not be interested in that report, an Apple Store or AASP will almost certainly be able to diagnose your Mac and are likely to draw that same conclusion.

Start here: Get Support. An Apple representative may be able to provide a diagnosis remotely, but the last step in drawing such conclusion will still require taking it in for repair.

Easy: Update macOS on Mac - Apple Support