“This Connection is Not Private” warning on Safari and Chrome

The warning means the website in question is not using — or Safari was unable to negotiate — an accepted encryption protocol.

Does it occur on one website, or all websites?

If Safari doesn't open a page or work as expected on Mac - Apple Support is an all-encompassing, if overly broad, checklist to follow that leads to a solution in nearly all cases. However, you have to methodically exhaust each and every suggestion, even those that may seem inapplicable or trivial. If you are unable to follow any specific step please identify which one.

I figure there is something I need to add or eliminate, but don't know where to start.

That's the reason you have to start with If Safari doesn't open a page or work as expected on Mac - Apple Support. Please don't omit any steps.

I have found that poor signal 📶 is usually responsible for websites to time-out or disconnect.

Just toggle Airplane mode on, then off to reconnect usually solves this phenomenon.

Good luck! 👋🏼😉