So I had this issue on multiple websites where I would connect Google site kit to my Google account which showed the Search Console data but would refuse to connect to the Google Analytics portion in the sections below.
I tried everything under the sun from linking the Analytics with the Search Console, to trying to login with all Administrator accounts for the WordPress dashboard and disconnect, delete Site Kit, flush cache, reinstall Site Kit, Activate & Reconnect, all for the same issue to keep happening for 2 hours.
/* What Finally Worked For Me */
I just deleted the Analytics property for the website and recreated it and it worked. Hopefully I helped save someone some time dealing with this issue. GL.
If you already had implemented tracking code either with help of any other plugin or by embedding code in header file manually, then you need to first remove code from there as it would conflict and won’t allow you to connect Google Site Kit to Google Analytics.