No, a cookie with default settings attached to https://example.com saying "previous_visitor=true" does not provide any information whatsoever to any sites other than https://example.com.

There are various techniques to place "cookies" (sometimes not technically cookies) that can be correlated by multiple websites working together, but the website has to go out of their way to proactively do that, this is not something that gets enabled by simply placing a standard non-personalized cookie.