Thanks for that reply, BDAqua. I've done as you suggested, and the Disk First Aid did seem to fix the immediate slowness problem, but it inevitably recurs so I also did the EtreCheck diagnostic. I'm just slightly offended that it had to mention that my late-2013 iMac is, in Apple's estimation, obsolete :(
I did install TunnelBear years ago and thought I had removed it but found it again today. Now I’ve moved it to the bin and emptied it but can’t be sure it’s all gone. They don’t provide an uninstaller.
As for antivirus software, I installed Malwarebytes years ago and it’s the same story: thought I had deleted it but can’t be sure.
I have these questions…
1 There were unsigned files and launch daemons from known applications, none of which sound dubious but I deleted them as I don’t use them: MicroSoft, Adobe and TunnelBear .plist files. Then I ran a second EtreCheck, which is the one attached as extra text.
2 I think I read somewhere that Java is verboten and to delete anything to do with it. I saw a file called com.oracle.java.Helper-Tool.plist – should I delete that?
3 I deleted a font app using their uninstaller, but there are 8 others listed as unsigned apps, all in Library > Scripts > ColorSync. Do they need to be deleted? ColorSync is part of the OS, isn’t it?
4 I turned off File Sharing and Remote Login.
5 As for the “Minor issues” listed – Heavy RAM usage, Apps with heavy CPU usage, Heavy I/O usage, Kernel extensions present – I have no idea what these even mean, so I do need your assistance here, please!
6 I haven’t used Time Machine for maybe 5 years or so, so I doubt it would be involved in this problem.