Tentative vote, based on what you've all been saying. Suggestions welcome. Might need to trim it down a bit.
[x] Call Kirika and Oriko, ask to come over, offer to bring groceries.
[x] Text Nagisa's uncle asking if it would be okay for her to come round today around 5.
[x] Practice roof-running on the way to the store and the way to Oriko's house. You've done these impossible mid-air momentum changes in battle without thinking, you know you can do it, try to tap into those instincts.
-[x] If they want groceries, get some groceries, and cake, and some ceylon black tea. If they don't, just the tea, it's a gift.
-[x] Ask her if Akiko is likely to recover ever without intervention.
-[x] Explain that there's a magical girl who goes around collecting soul gems, mention possibility of raid on gem collecter girl in the future to make her stop and possibly save her captives.
-[x] Talk about eventual possibility of the Meguca Hotel being a thing. Now that Sabrina's here, there's no more reason girls have to fight than normal people. We can break the system.
-[x] Enlist her and Kirika's help to spot us while we science. Kirika can antimagic pulse if things go wrong, Oriko can tell us if things are likely to go wrong.
--[x] Pump healing magic into a clear seed. Try to focus on healing the girl within, pay very close attention to any small changes to the seed or if anything materialises nearby.
--[x] Try to make a witches barrier. Focus on the feeling you got when you studied them before.
Edited to change if akiko will "wake up" to "recover".