Question on No index website

I have two websites. One is index and ranking in SERP. The other website is no index. Now, if I am redirecting a user from my index site to a non-index site. What kind of information does google catch? I want to hide all the details related to no index site completely. So is it safe to still redirect the user?

Redirecting can drop the referring domain, so you could use server side redirects, avoid JS redirects altogether, or try modifying the JavaScript so that the referrer isn’t dropped.

Google crawlers are allowed to crawl noindex pages/sites,
blocking the crawlers in robots.txt is the way to go, this way, they won't be able to crawl it in any way,

apart from this, I don't believe they will track you using the google SEO crawlers,
but browser tracking is a totally different thing