I've done this beating myself up nonsense and I'd say you need to not do that, that won't help your mental health. Your daughter is fine! To her this is probably a great day, no hassle, cartoons and a couple of treats plus a book! Far from neglectful.
Days like this cannot be helped and you will probably have them again when you have a bad cold etc. The best thing I did on those days, that made me feed better about it, was provide more snacks. Snack plates are great. Blueberries, strawberries, babybell or cheese, mine likes olives and hars boiled eggs, cucumber, tomatoes, breadsticks, carrots, cold meat, a few spoons out of a tin of sweetcorn. All things that can be thrown together in seconds no cooking or thinking. You can do several eggs at a time and store in the fridge in shells. And it looks great on the plate you will feel better with little effort ! (I also do these after school when dinner is miles away) jars of pesto or Tom puree also great to store to throw in pasta. Yougurt, single jelly, Choc brioche rolls for treats after. Just make sure age appropriate size bites. Bring her upstairs and you lie down while she has a "picnic" on the floor. Tell her to bring some teddies.
I know you followed up with the fact your awaiting a food shop so sometimes we have to improvise. She is only 20 months she is unlikely to eat that much now anyway. Shes not burning many calories on this chilled day. Some milk? Get hubby to help with a better dinner.
Your doing amazing, and the fact your worrying about 3 hours of TV affecting her development is a sign of a really good mum.
I gave birth 3 weeks ago so I KNOW WHAT YOUR GOING THROUGH. And while I breastfeed for the 700th time today my other child is watching TV with a snack plate and shes is also more than fine.
There are many other days to come and many opportunities for you, when your well to be a fully engaged parent. That's not today and THAT IS OK.