Oh FS, I wish I could do the same thing to you I do with my bestie to cheer her up.
I text her ridiculous GIFS all day long at work. Silly ones, slightly flirty ones, GIFs just saying "hey!" so she knows I'm thinking of her during her rough day(s).
I know that funk well that you are in. It has visited me many times. Use it to stay caught up on sleep if possible, and allow yourself to be in it without guilt. It will pass because you are not the type of person where this is your normal way of being.
Do you like puzzles? Sometimes doing a puzzle when binging tv is one of those nice things to be engaged in something while relaxing. It also might encourage D13 to be present while not being required to talk. Talking for angsty teens is not what they want to do, for sure. Would it encourage her to pause and put in a piece or two each time she passed by? I'm a strong believer that sometimes people need things to do with their hands in social situations (spoken like a true introvert, huh?) to feel like they can be there without pressure.
Ok for today's silly GIF I send you one truly out of left field....Thumper on Ice. You know, from Bambi? See if you can find a GIF of Thumper sliding and spinning on ice and laughing. That's the random one I'm sending you today just for silliness.