Oh, I've been down this road more times than I care to count. One client redesigned their site without telling me - assumed it was purely cosmetic. Cue two weeks of panicked SEO triage.
If your client is sticking to a pure redesign (no IA changes, same status codes for existing pages), here's what I'd double-check based on painful experience:
First, compare Core Web Vitals before and after. Staging environments can reveal trouble before anything goes live - I once spotted a massive CLS jump from a lazy-loaded hero image that wasn't there in the mockups.
Second, watch internal links like a hawk. Redesigns love to silently strip out breadcrumb links, footer paths, or that sidebar you rely on. Ask for the Figma file and trace every link manually. It's tedious, but catching a broken internal chain before deployment saves your rankings.
Third, make sure the devs aren't using HTML tags for styling. I've seen H1s turned into H5s overnight because someone decided the new font size looked better with a different heading level. Insist on a tag audit in staging - check every main heading matches what's live.
One more thing: test your main pages on the staging environment with a proper crawler. Clients love to say "it's the same" until you point out the meta description is now an empty string.