Does it make sense from an SEO point of view to change the design and text content in two steps?

Question

Search Engine Optimization

I am updating an online store, during which I need to move to a new CMS and heavily (80%) rewrite some information pages (articles about products). On the new CMS, the design will change a lot, "imitation" of the appearance of the old CMS is not planned.
A couple of articles have a good SEO effect that you want to keep as much as possible.
As far as I understand, on pages with rewritten articles on the new CMS, it will be correct to keep the following:

1. URL like on old CMS
   
2. Tag content <title></title>, <meta name="keywords">,<meta name="description">
   
3. Those successful sentences that have popular keywords and are visible in the search engine snippet (each article has one such sentence)
   

The question is, does it make any sense in such a situation to update the site in two stages: first put the updated text in the articles on the old CMS, wait for search engines to reindex, then update the CMS (at this point the design will change)? Those. try not to "scare" the search engine by simultaneously changing the design and text surrounding relevant offers, and smooth the transition. The answer suggests itself "it won't get worse", but you need to spend time on this - a week or two, until you wait for the robot, that's why I'm asking.

Answer 1

The search engine doesn't care about your design.
Change when you want.
It’s better to do it right away on the new CMS and add new articles there after the transfer.

Answer 2

I would recommend doing this
1 update everything at once.
2 Immediately after replacing the site, add it to the Yandex and Google webmaster panels.
3 for the peace of mind of the customer or yourself, so as not to lose anything at all, or if you lose, immediately understand what is lost ... make tracking 404 pages. For example, through google tag manager. I usually do it like this www.lunametrics.com/blog/2014/08/19/404-errors-goo...
4 check robots.txt + sitemap.xml