Thank you for clarifying the version of macOS being run on the computer El Capitan.
User wrote " I really do tire of this relentless push to update " well, as Technology Changes and Certificates Expire - one may move forwards or get left behind, as Bob Dylan has been quoted " The Times that are a changing "
There are options to get around this. That is by upGrading - installing a newer version of macOS. All this without having to " fork a cool grand or more to replace our laptops "
Below is a possible solution - from one retiree to another -
The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.
With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. For Best results use Safari to commence the download as Others may not work.
Make a Time Machine Backup it very useful and can be used to Revert to Previous Working macOS Before attempting.
Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina & Big Sur supports only 64 bit and there is no workaround.
Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.
Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation