Safari repeatedly asks to confirm not a robot

That is not Safari, but rather a form of security captcha filter that the visited site uses. Facebook tends to use this to annoying degree in one group I visit.

Some sites are satisfied with just checking the "I am not a robot" box, while others force you into identifying multiple objects in a segmented image, and may present multiple occurrences with other images before granting access to the site.

Websites that rely upon (or exist for the sole purpose of) harvesting personal information will object to Safari's privacy features such as intelligent tracking prevention. Poorly coded websites (i.e. most of them) will then erroneously conclude the website request was automated as though originating from some automated service or "bot". Hence the annoyance.

That's just the beginning, since if you use some of Safari's more advanced privacy-centric features such as iCloud Private Relay they are almost certain to object, and might even refuse to load. Why should they — if they can't extract 💰 from you then you don't figure into their business plan.

You have to decide which you value more: your privacy, or the website.

References:

https://webkit.org/tracking-prevention/

https://developers.google.com/search/docs/fundamentals/seo-starter-guide

About iCloud Private Relay - Apple Support

Safari Privacy Overview - Apple