Except people in a typical company who might provide quality feedback on the new website, do not want to "browse Figma". They want an actual website to view - dev site or the actual new live site.

> "You can't just launch a new website and surprise your team."

Yes you can. Nothing beats launching a new site to motivate quality feedback. If you expect feedback to arrive soon after launch, you can use this to your advantage.

If you like the sound of crickets, share a link to Figma and ask people for feedback. Designers and developers will respond, others like sales and non-technical staff often won't. Why? Because people prefer the security of their web browser's familiar reference point when assessing a website. As opposed to browsing an app that gives them a special window to a slippery canvas where an impression of the website is found.