It looks like your Mac is compatible with
OpenCore Legacy Patcher. It's an app that allows to run the latest versions of macOS on unsupported Macs.
Basically the app runs you through downloading a macOS installer, putting it on a USB memory stick, then patching that memory stick to allow your unsupported Mac to boot from it and install from it.
I'd recommend you to get an external drive and make regular Time Machine backups (if you don't use one already). I use OCLP on a 2012 Mac mini so I can use it as a file / media / music server. One one occasion it failed to boot after an update, but I was able to restore it from a backup and was back up and running in an hour or two!
From what I can tell you cannot update your current install to a newer version of macOS, so you will need to do a fresh install. I believe however that you can upgrade to newer versions once you are running a patched version of macOS, although I haven't tried upgrading my Mac mini to Sonoma yet.
There are threads on these forums, plus a Discord server where loads of helpful folks can give you advice and help if you need it.