In 2021, I ran a two-team, two-codebase detangling project with 20 engineers. Both codebases were writing to the same database, but one was the leader for some fields and the other was the leader for the rest. It was causing serious production issues in a highly regulated field, so we fixed it as fast and accurately as possible with almost no downtime. The very first thing was building in automated error detection processes so we could have product staff catching and fixing errors live.
We split the work into six releases over six months. Separating the two systems required a totally different architecture with a significant amount of code changes in the one system.
We didn't exactly use this method step by step (I hadn't heard of it). We thought logically through all the steps, and then reversed them. There were spike branches that we used to gather all the steps, and then we did delete them. But we only used maybe 4 or 5 spike branches total. Unit tests didn't drive anything - these changes were more system-integration level, so there weren't existing unit tests we could use.
In the end, it worked, we made a major overhaul to the one system and updated the second to now be the leader on all. We built an API on the second system, so it could be called by the first when new records needed to be created.
So I'd say, conceptually this method is what we used, but really none of our to-do list was generated from unit tests. Perhaps we could have built out a ton of tests and separated it into a release every week or every day, but we felt comfortable with the monthly releases. That helped because the QA process was pretty long (a lot of features in a regulated industry). Each release they were testing for at least a week. That being said, we built out a lot of unit tests to complement the changes, and I don't think QA found any issues in any of the six releases.
As the author described it, Mikado method is recursive. You find a to-do list on the first branch, then possibly more things on the second branch, and more things on the third. We only did one "loop", maybe two, where the author might do many.
I got this by thinking about the Kent Beck quote "first make the change easy, then make the easy change".