What gets lost most often in a redesign?
Rankings, and almost always for the same reason: the URLs change and nobody planned the redirects. It is avoidable damage, a spreadsheet and a few hours of work, and expensive to reverse because recovery takes months.
The second thing lost is the measurement history, when analytics gets reinstalled without keeping the event and goal configuration.
How do you know whether the problem really was the design?
By comparing conversion per channel before touching anything. If direct and organic convert reasonably and campaign traffic does not, the problem is the ad's promise or the targeting, not the site.
If no channel converts, the site is the suspect, but it pays to tell design, message, and friction apart before commissioning a redesign that only covers the first.
Separating design, message, and friction is what we deliver in a Digital Audit, and it usually saves a good part of the redesign that was about to be commissioned.