KiltedTim has already given you the answer, but I will try to expound on it a bit so you have a better understanding why you will need to upgrade your Mac to a newer model if you want to continue to use the Internet to access secured websites.
You're running into a Google OAuth 2.0 security requirement issue because Google has deprecated support for older authentication methods and insecure browsers. Since you're on macOS High Sierra (10.13) on a mid-2010 iMac, your operating system and browsers are outdated and no longer meet Google’s security standards.
Currently the minimum macOS version required by Secure Google Authentication is: macOS Catalina (10.15). For reference, High Sierra is two versions older than Catalina, and seven versions older than the currently latest version of macOS: Sequoia. It is important to note that Apple only supports the last three versions of macOS for security updates. That currently would be (in order of newest-to-oldest): Sequoia, Sonoma, & Ventura.
In addition to the operating system, Secure Google Authentication, has minimums when it comes to the web browser you use to access it ... and they are:
- Safari macOS 10.15+ (Safari updates are tied to macOS updates)
- Google Chrome Version 91+ (May 2021)
- Brave Version 1.25+ (based on Chrome 91)
- Firefox Version 90+ (July 2021)
My suggestion/recommendation, if you want to continue to access secure websites, would be to upgrade to a Mac that can run Catalina ... but, better still, to get one that can run one of those three latest versions.
For the iMacs:
- Oldest model that can run macOS Catalina: Late 2012
- Oldest model that can run macOS Ventura: 2017
- Oldest model that can run macOS Sequoia: 2019
