Most redesigns that damage search performance do so for the same handful of reasons, and every one of them is visible before launch if somebody looks. This is the checklist worth running through with whoever is building the site.
Is there a redirect map for every existing URL?
Not the important pages. Every URL that currently returns a 200 and has ever earned a link or a ranking. Ask to see the file. If it does not exist two weeks before launch, the launch date is the problem.
Does the new site keep the content that earns the traffic?
Redesigns tend to shorten copy for visual reasons. If a page ranks because it answers twelve questions and the new version answers four, the ranking usually follows the content. Compare word count and covered subtopics page by page on your top pages.
Who can edit the site afterwards?
A site your team cannot update becomes stale within a year. Before sign-off, have a non-technical person on your team add a page, change a headline and upload an image while someone watches. If they cannot, the handover is not finished.
Has anyone tested it on a real phone?
Not a browser window resized to phone width. An actual device, on a normal connection, filling in the contact form. Most mobile conversion problems are discovered this way in under five minutes.
None of this is complicated. It is just easier to check before launch than to diagnose three months afterwards, when the traffic has already gone.