301 redirect from new site to old? : SEO

Hey, so we have an existing site with strong domain authority (let’s call it domain A) and will be creating a new site (domain B) that extends our existing app functionality. Domain B will be absorbing a lot of traffic, but all of our relevant marketing materials are on the primary domain.

One of our developers suggested we use a 301 redirect to let Google know that traffic flowing into Domain B should feed back into the domain authority of Domain A. However, when I looked into this, it seems like everyone talks about using 301 redirects to pass traffic from old sites to new ones, and not the other way around. He countered this and said that it’s all about setting up a canonical URL and doesn’t matter which one came first.

If we set up a 301 Redirect from domain B to domain A, will that literally redirect them to the old page or just act as a signal to the SERPs? Also, is there anything we should be aware of or cautious about when doing this?