I had done this quickly back in October when I first tried out the ParseJSON() function in PowerApps, but hadn't gotten around to documenting it up. Then when I went checking to see what everyone else had written up I saw that Shane has done a video on this. Oddly enough, we both approached this nearly identically.
However, I'm dropping this here for posterity and because I always like to read my own typing vs. listening to anybody else's voice. ;)
If you have solved grabbing lots of records from "somewhere" (i.e. SharePoint) and returning it to your PowerApp as a bundle of JSON using Power Automate, the reverse is now what you need to solve for. Fortunately, writing out a lot of updates is similarly easy, but also similarly obtuse per guessing exactly how to get it done. Here's the Q&D on how to make it happen.