Mac Mini screen glitch followed by fan noise then reboot
It is likely that the macOS upgrade you did recently is coincidental.

The symptoms you describe lead me to think that the issue is strictly hardware and will need examination from a tech conversant with troubleshooting Mac hardware.

It could be a 'graphics card' issue but as the graphics card is integrated on the system board and not a separate item that is separately replaceable (though there are some independent techs who do such work) it is more appropriately referred to as a system board failure.

So, time to take it in for service. A local Apple Store, Apple Authorized Service Provider or Apple tech of your choice.