I have experience in migrating large DBs with replication and the article not discussing write blocks made my ears perk up as well.

Aside from the blocking you mentioned during the initial snapshot, you'd need to block writes to the old DB before the cutover as well. There's no way to guarantee in-flight writes to the old DB aren't lost when promoting the replica to a primary otherwise. I'm surprised the author didn't go into more detail here. Maybe it was fine given their workload, but the key issue I see is that they promoted the new DB to a primary before stopping the old application. During that gap, any data written to the old DB would be lost.