I have IMac w/MacOS High Sierra (recently updated) w/Safari 13.1.2

Sorry you are experiencing this frustrating situation. You should know that Safari is installed as part of the operating system and it normally it cannot be individually upgraded. It is periodically updated when the computer's operating system is updated or upgraded. Yours is not an unusual situation. The reason is that web site engineers write their software to work with specific browsers and specific versions of them. You can hope that your web site's developers eventually update their site to work with Safari, or you can use another browser that does work on those sites such as Firefox or Chrome. They can be individually updated as needed. Finally, even if you are able to update Safari, there is no guarantee that it will be compatible with every web site. I hope this information is helpful.

I'm glad things have improved for you, but I have a couple of comments to share. What I've tried to explain is that when a web site isn't able to be properly opened, it is not the fault of Apple's browser. It s because the site developers have not written their code to comply with Apple's requirements. There is no way that Apple, or any other browser provider, could write their codes to match the many thousands of web sites out there. Apple and the other browsers publish what their interface requirements are so the web sites can work properly. And some never will. This is why many of us use additional browsers such as Thunderbird or Chrome. I hope this helps you to understand why these thing happen. Enjoy your OS upgrade.