How do I fix a slow iMac 2017 running macOS 13.7.6?

More than likely the internal Hard Drive is failing. The other common cause is an issue with third party installed software.

To check the health of the Hard Drive you can run DriveDx (free trial period) and post the complete text report here using the "Additional Text" icon which looks like a piece of paper on the forum editing toolbar.

To gain more information about the system & possible issues in general, run the third party app EtreCheck and post the complete report here so we can examine it for possible clues.

How to use the Add Text Feature When Posting an EtreCheck Report - Apple Community

FYI, Here is an Apple article for steps the user should follow when selling or disposing of a Mac:

What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

Unfortunately that article doesn't address the security & privacy issue of user data still being accessible on a Hard Drive. You have two options for making sure the user data is made inaccessible to anyone who gets hold of the Mac later on:

1. Enable Filevault and let it finish encrypting the Hard Drive. Once Filevault has finished encrypting the Hard Drive, then you can follow the instructions at Step #6 in that linked article for a simple erase of the Hard Drive.
2. Use Disk Utility to erase the drive in Step #6 of the linked article, but also select the "secure erase" option where you can choose to write zeroes to the whole Hard Drive which overwrites all your data.

Both of these options may take a day or more for a healthy 1TB Hard Drive, but could take multiple days if the drive is failing (or it may not be able to complete).

Also, I highly recommend you create a bootable macOS USB installer now while you still can if you wish to reinstall macOS onto this iMac. If the internal Hard Drive is failing, then installing macOS onto an external USB3 SSD (& booting & using from the external) will allow you to keep using the iMac. When even this is no longer needed, then you can re-purpose that external SSD to another computer as a data drive or backup drive.

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

This will be inherently slow as the drive has a Rotational Drive with all kinds of move parts

Where as an SSD Drive would be way faster

If you what to extend the like of this machine and spend some money

Explore www.owc.com for a good Enclosure and a compatible SSD drive

Install the Operating Stem to the drive and make the external Drive the Startup drive

2 - As mentioned by @BDAqua >> CleanMyMac aka BrickMyMac is a popular Third Part Disk Cleaner that is know to cause a lot of issues

Any of the below should be removed as per Developers Instructions 

Disk Cleaner 

CleanMyMac , aka “ BrickMyMac “

New macOS Malware "Cthulhu Stealer" Targets Apple Users' Data

Un-Like Microsoft Windows, which does have “ Disk Cleanup “ and “ Defrag “ as part of their Operating System 

Apple does not  nor are that needed

Even if the drive isn't failing, that "Medium Type: Rotational" suggests that the OP has either

• A slow 1 TB 2.5" 5400 rpm mechanical hard drive, or
• A slow 1 TB Fusion Drive that pairs such a hard drive with an inadequate amount of SSD space.

Getting an external SSD and using it as a startup drive could help. That iMac has USB-A (USB 3.0) and USB-C (USB 3.1 Gen 2, Thunderbolt 3) ports, and so is compatible with a wide range of external SSDs.

it's not a clutter problem.

That iMac has too little real RAM memory to run Ventura and later in an appropriately-responsive way. To make things worse, its internal drive is likely a simple a Rotating Magnetic drive, or a two-part Fusion Drive, so when you run out of real RAM (because too many apps have too many windows open) that needed RAM gets simulated on a drive that is now considered glacially slow..

RAM can be expanded to as much as 64GB. Comparable SSD drives are available that are at least four times faster.

Although these aftermarket upgrades are available, all such upgrades require cutting the display retaining tape and removal of the glass portion of the display on that model. Much more specific information is available. If you want it just ask.

EDIT: I was watching the videos on how to do those upgrades, and they are suitable ONLY for those who a Very Handy. While I was watching, others answered most of your questions. My writings were made before those others were seen by me, NOT intended to diminish them in any way.

Uninstall Clean My Mac and get an external SSD to boot from.

We might be able to help figure out what’s going on with your Mac. It could be anything from an unintentional malware installation to a hardware bottleneck or failure. Some things are fairly easy to fix.

Please run an EtreCheck (free) evaluation of your Mac and post the generated report back here in a reply. EtreCheck is a safe and highly regarded utility from a trusted developer and respected ASC contributor. The report it generates will not include any personal info. It simply gathers specifics about hardware performance and installed software that might be in conflict with the OS.

Please navigate to EtreCheck.com to download the utility. Once you’ve run the app and created your report please post it with your reply to this message. 

Please note you must upload the full report. To see how, please click >  How to use Add Text when posting… EtreCheck Report.

We’ll use your EtreCheck report to look for the things that may be causing your problem and advise how to correct them.

Best use might as a trade-in. Check the Mac trade-in site to see if this Mac is still valuable toward a newer model.

https://www.apple.com/shop/trade-in?afid=p240%7Cbi~cmp-698200233~adg-1243548979435089~ad-77721944069409_kwd-77722184077779%3Aloc-190~dev-c~ext-~prd-~nt-search~crid-&cid=aos-us-kwbi-mac-account-launch-040725-

Just enter serial number and answer questions about condition honestly. You are not committing, and you can quit out of it at any time. Let readers know what you learn.