How to speed up my iMac running macOS 12.7.4

Well it is likely slow due to the 5400 RPM HD that is installed. At their best they were glacially slow, however your HD may be failing which would make it even slower. My advice, before you do ANYTHING backup using Time Machine to preserve your data. If you do not and the HD fails your data is gone, permanently!

After you have backed up the please do the following:

It will help us get a good idea of what is causing your problem if you provide a report of your system, that way we do not have to play 20 questions with you. The report we are requesting does NOT provide any personal information and is extremely safe to use. Please navigate to www.Etrecheck.com and download the free version of EtreCheck. Once you have you downloaded the app and installed it, please run the report and save it. This report will help us get a good idea what has been installed on your system and help us be able to diagnose what may be wrong.

When you have your report, you can attach it when you reply to this message and we can then review it and help you determine what is needed to get your system running well again. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message please click How to use the Add Text Feature When Post… - Apple Community It is helpful to us if you download the report to your Desktop.

After you post your report we can see if there are obvious software problems that are causing the slow-down and if the HD is failing that may show up too.

I am running the same OS on a 2015 27" iMac with a 256 GB drive and 16 GB of memory. I agree that the first step would be to make a Time Machine backup. I recently reformatted the drive, reloaded the OS and kept any additional software to a minimum. You might want to check System/Users & Groups/Login items to see if you are loading too much as the computer starts. My computer boots nearly as fast as my M1 MBA. I credit a lot of the speed to the 16 GB of RAM.

Adding RAM does not speed up a computer that a user can perceive. Your 256GB drive is likely a SSD which is why your computer is quicker. The OP's computer almost certainly does NOT have a SSD installed, at best it may have a Fusion Drive which relies on a 5400 RPM HD which I suspect may be failing.

In order to get anything useful the OP should post an EtreCheck report of their system and also a DriveDX report on their HD. Anything else is just conjecture.