You are correct, Windows 11 S Mode is a Microsoft function, not a HP function.
If your Windows 11 version has not been updated in 2 years, that indicates your Windows 11 version is no longer supported and that makes your system less secure.
S Mode in Windows just limits you to installing apps from the Microsoft Store, and most people do need to switch out of S Mode to install the apps they need, and provided you only install apps from the developers website, then switching out of S Mode will not lower the security on your system.
The problem is, most troubleshooting steps to resolve Windows updates do need you to switch out of S Mode, and because your Windows 11 system is so much out of date, most likely you would need to use the Windows 11 ISO to upgrade your system, and that cannot be done if Windows is in S Mode.