Website functionality in Safari is deteriorating

The problems you describe are going to occur with increasing frequency, as websites continue to demand newer browsers. Those newer browsers often require newer operating systems, which in turn often require newer Macs.

That story will never end. Fortunately browsers themselves are becoming obsolete, and will — eventually — fall out of favor.

... on its landing page it advises that it does not support Safari and to use Chrome instead.

Pardon my language but the heck with that idea. Anyone willing to infest a Mac with Google's garbage should not be using a Mac at all.

In the meantime you may want to consider using a browser that continues to be updated, such as Brave:

https://brave.com/

It is updated routinely and will work just fine on your twelve year old Mac.

Many websites face issues with Safari as they favor newer browsers and operating systems. Your iMac, running High Sierra, can't upgrade further. While some sites suggest using Chrome, you resist due to preferences. This trend may persist, but the story might change. Browsers are evolving, and alternatives exist. For now, you must be using Firefox but you need to use some other ways. In the meantime, opting for a regularly updated browser could be a practical approach to ensure compatibility and a smoother online experience, even if it means navigating away from Safari. Thus, you can use either brave or microsoft edge as they are the best alternatives instead of chrome.

[Edited by Moderator]

I also have this problem, but they also do not open properly on Chrome.

They will only open on Firefox.