My iMac is 10 years old and no more software updates are available

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.

Safari will open a redirect and open the Apple Store where the download can commence.

macOS Big Sur 11 hardware requirements

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

macOS High Sierra 10.13 hardware requirements

macOS Sierra 10.12 hardware requirements

Caution - jumping over all the newer versions and directly to Monterey on Qualifying computers is Technically possible - there are those who have attempted and were successful. Then there are those who attempted and had less than good results.

If this is a Production or Mission Critical Set-up - a more prudent and measure approach is suggested. 

The above is from observations on the Apple Support Community Forums and IMHO

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey 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

..philipsburger:

Perhaps to view this Apple support upgrade article and see the compatibility information,

and based on your Mac's build model year; then choose if it could upgrade to newer OS.

• How to get old versions of macOS - Apple Support

https://support.apple.com/en-us/HT211683

An older 24-inch early 2009 iMac was given me a few weeks ago. I'm not sure if a thought

was included in that as well; however I was able to update the encryption certificates to

make it OK for the short term. ~ And El Capitan 10.11.6 is its last stop on the upgrade hwy.

This older iMac, not without other issues; that said, it's still a good internet music player.

Was able to add newer secure items to self-approve, from Let's Encrypt site, for El Capitan.

Those also helped a later Mac, running High Sierra. (Firefox ESR has sunsetted on 10.11.6)

There are a few resources online, some good for a little while. Like fresh produce.

Instead of saying "ten years old," pleases do "About this Mac and tell us the actual year, with any modifiers like Early, Mid, or Late . Example from El Capitan:

Why? A mid-2010 iMac will run High Sierra and get around the obsolete certificate issue that you and many other usees of obsolete OS version are seeing—and it is nearly 12 years old!

It will still be obsolete but newer browsers versions that work with High Sierra should not have issues the the security certificate issue. Still, the handwriting on the wall. If third-party developers are going obsolete such older tools, soon High Sierra support will be gone.

If you can upgrade the OS to High Sierra, that will buy you some time, that's all.

Ref: https://letsencrypt.org/docs/dst-root-ca-x3-expiration-september-2021/

The above developer of certs sells to a LOT of other developers and, based on reports like yours here, Cloudflare as well.

With due respect it may be time to replace the computer with a newer model. If El Capitan is the latest it will run it is closer to 13-14 years old!

What you are is experiencing is the tip of the iceberg in compatibility and will not get better.

I believe researching a replacement would be the best course to take.

I will second the comments above. Also, I am not familiar with Cloudflare, but most 'security' apps do not work well with Macs and often cause a variety of problems. As to Safari, I would install an additional browser to use when necessary such as Firefox or one of the many which are available from the Apple App Store.