To answer the question for those interested, "Do I need to watch these to enjoy/get the full story of Yesterday wo Utatte?" I would say 100% YES.
In fact, even though I didn't enjoy the show that much, the scenes included in this ONA are ESSENTIAL to understanding changes in the plot, certain character motivations, and even the ending of the show. Each episode of the ONA corresponds to an episode of the main series, I would recommend looking them up so you know when to watch them. I say this, because there's honestly scenes that should've been in the show, but they probably ran out of episode air time, so they animated them anyways and uploaded them online instead.
Nevertheless, it leads to confusion in the long run if you don't watch them so do so; especially if you like the show but heck even if you don't, they'll include plot that is canonical and will get referenced later. I warn so there are fewer people in this world who waited to watch them until the show ended (like me), and because of such, were really confused about some things. Honestly, my issue with the ONA is having essential content be outside of the show it's associated with is a bad meme that I hope doesn't stick around.