Suddenly, extremely long file copying times!

I agree with the direction @Matti Haveri is going, but I think it requires looking inward at the internal Hard Drive your iMac most likely has. If emptying the Trash is slow of your boot drive is slow, that indicates a problem with the internal Hard Drive (Fusion Drive), or an issue with third party software, or a file system issue.

You can easily check the health of the internal Hard Drive by using the third party app DriveDx (free trial period) and posting the complete text report here using the "Additional Text" icon which looks like a piece of paper on the forum editing toolbar. I will gladly examine the report for any possible drive issues. If you have a Fusion Drive setup, then make sure you include the report for the Hard Drive portion of the Fusion Drive since it is unlikely the SSD portion is the problem....the HD portion tends to be the 2nd "Macintosh HD" item on the left pane of DriveDx, but you still need to confirm.

What kind of drive are you copying to?

HDD? SDD? thumb drive?

How is the drive attached to the iMac?

Directly? via a USB hub?

Assuming it's USB, check System Information.app and look in the USB section. You should see the drive listed along with it's connection speed (typically 1.5Mb/s, 12Mb/s, 480Mb/s, 5Gb/s or 10Gb/s depending on connection type and device capabilities). My guess is that the connection speed is lower than usual/expected, and answers to the above questions may shed some light and troubleshooting ideas.

You’re getting good advice here, except for one detail:

do not follow any of it until after you have a complete and current backup

If the hardware is failing, you may well not be able to even get a copy of your data as the failure progresses.

Failing disk? Bad cable? Bad USB hub or dock? Unnecessary 3rd party virus app or cleaner?