Upgrading MacOS beyond Ventura on a 4.2 GHz Quad-Core Intel Core i7 with Radeon Pro 580, 16 GB RAM

Nope, the 2017 year model iMac's can only run up to macOS Ventura.

see > Identify your iMac model - Apple Support

Here are the Macs that support Sonoma, which is the next OS version after Ventura:

• iMac (2019 and later)
• iMac Pro (2017)
• MacBook Air (2018 and later)
• MacBook Pro (2018 and later)
• Mac Mini (2018 and later)
• Mac Pro (2019 and later)
• Mac Studio (all models)

You can find the model name and year of your Mac by going to the Apple menu and choosing About this Mac.

You need a 2019 or later iMac to upgrade beyond Ventura.

Nils Svanberg wrote:

Is this because of the processor or simply because of the age of the iMac?

macOS update versions hinge on the year model, not the processor spec's.

If you can't afford to upgrade your Mac may you should consider an alternative to MS Office: LibreOffice , It can open edit and save MS Office documents to the MS Office formats/extensions or its own format. And it's free!

Regardless of the hardware specifications, it really comes down to what Apple decides to support (or not,) since they "own" the macOS license ... and running a version of the OS, that was not designed to work with that hardware, could be a potential user violation of that license.

Microsoft Support – Upgrade macOS to continue receiving Microsoft 365 and Office for Mac updates

"What if I don't update macOS to a supported version?

If you're on an unsupported version of macOS, your Microsoft 365 apps will still work but you would no longer receive any updates including security updates. For example, if you're on macOS Monterey, but later you don't update your macOS to a supported version when macOS Monterey is no longer supported, you won't receive any updates of any kind."