Your 24-inch M3 iMac is compatible with macOS 27, so the M3 chip itself should not be the problem.
Apple currently lists macOS 27.0.1 as the latest release. Apple — macOS 27 compatibility
Since Software Update is showing macOS 26.7 as the latest version instead of offering macOS 27, the first thing I would check is whether macOS 27 is actually being made available to your Mac.
There is no need at this stage to assume that RAM, storage, Microsoft Office, the VPN or your internet connection is responsible.
Open Applications > Utilities > Terminal, enter: softwareupdate --list-full-installers
and press Return.
This simply lists the full macOS installers currently available for your Mac; it does not install anything. Apple — How to download and install macOS
If the results include 27.0.1, we can then try downloading the full installer directly with and in Terminal:
softwareupdate --fetch-full-installer --full-installer-version 27.0.1
This downloads the full macOS installer but does not immediately upgrade your Mac.
I would wait until we see the --list-full-installers results before running this command.
If 27.0.1 is not listed, do not run the download command.
The absence of 27.x from the list would itself be useful information about why the upgrade is not being offered.
Please paste the complete Terminal output here, along with the exact wording shown under > System Settings > General > Software Update.
We can then decide whether downloading the full installer is appropriate.