If you're hoping to participate in the SEO game, you have to utilize google's javascript analytics code. Their code collects and reports on a variety of user activity. It's safe to assume (based on google published articles [1]) that the data collected is used to influence the site's rankings.
You don't need to install Google Analytics to rank on Google.
The article you cited mentions CRUX data[1], which comes from the Google Chrome browser, not Google Analytics. That data is reported to website users in the form of the Core Web Vitals report, which is a different product than Google's ranking algorithm. Although similar data is probably used as a ranking factor, you can't conclude that from this support documentation.
1. https://support.google.com/webmasters/answer/9205520?hl=en