Nope, it has reached the end of the road for updates. As far as the sluggish behavior is concerned then the only thing to do at this point is to try and found out why. I suspect at 12+ years old it may be having hardware issues such as a failing drive. 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 towww.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.
If you cannot afford another iMac I would strongly suggest looking at the new M4 based MM which would be a HUGE upgrade over your current machine. For less than $1400 ( $999 for a MM with 16GB RAM and a 1TB SSD + $300 for a vert nice display) you have a very very nice solution. Also, did you know that Apple offers 12 month no interest financing, so the $999 can be amortized over 12 months or about $83 per month. You can also use the old iMac mouse and keyboard so the < $1400 is very real.