Will a system update speed up my iMac?

If you have a problem, an update will not solve it; in fact, it may exasperate the problem. You need to find out and fix - if possible - the problem first.

So, you have a 21.5” iMac? If you have the default snail like 5400 rpm hard drive, there is part of your answer. An i3 processor is ok, but about the slowest nowadays. And, 8 GB of RAM is considered on the low end, especially if you run resource hogging things like Chrome and Adobe.

You might want to consider downloading and running etrecheck report and posting it here using he third little icon from right in the toolbar to post it here.

My 2019 iMac running Mojave (10.14.6) is maddeningly slow—slow to boot, slow to open apps.

Those are classic symptoms of the slow factory hard drive issue babowa mentions.

I agree completely that upgrading the OS now will NOT make this better, and could very likely make it worse without chasing down the root causes of "slow."

Posting a EtreCheck report here as babowa has wisely requested has two great benefits to this issue:

1) It applies hard numbers to drive performance, providing real data to what are now general assumptions about the issue.

2) Etrecheck wit spotlight any third-party apps or utilities that are known to degrade performance.

and it does so without giving away any personal or security information.

The basic version of EtreCheck is in the Mac App store at no cost: https://itunes.apple.com/us/app/etrecheck/id1423715984?mt=12

If you need more help with how to work with forum limitations when posting the report, this User Tip is quite good:

How to use the Add Text Feature When Post… - Apple Community

I fully agree with the comments made. I would add some thoughts. Firs, upgrading to Catalina may slow things down even more as Catalina is known to use more RAM than some older operating systems. Second, your Chrome browser is a RAM hog. You might consider using another, such as Firefox or Safari.