After updating Catalina 10.15.7 I was no longer able to open several important (to me) sites that I use for business, eg, eBay etc. Please advise.

First please restart in Safe Mode ( Use Safe Mode to isolate issues with your Mac ) and then restart normally and test. If that does not work, please let us know.

There have recently been many reports of a broad range of new problems on this support site about the latest release of Safari v15. It is included in the downloads for Big Sur and Catalina. If you are experiencing these problems, you can use another browser such as Firefox or Chrome and they will work for you until a newer version of Safari is released.

I have read here that Apple's support people have a link to reinstall Safari and that doing so often fixes the problem. You might check with them.