The re-branding is relatively surface-level ( non structural )
You want to release it all at once
The total amount of time for the rebranding will take a few days or weeks at most
In that case I’d take this approach;
Get everything you need for the re-branding ready- logos, color palettes, icon selection, etc.
Then-
Clone your site
Rebrand the clone
Any content changes you make to the main site during this rebranding period you must also make to the cloned site, to keep it in sync. That means double-publishing blog posts, etc.
When you’re ready,. transfer the site plan and domains to the cloned site, and it’s live
That will give you the least wasted effort and no disruption to your production site.
Your assumptions are correct and I agree with your approach. We will go the cloned route. PS. Here is our site if you want to peep: https://www.prismatic.so/