I'd watch it with the sweetener. Depending on the sweetener you use, it might raise your insulin levels (that's the case with aspartame for instance, the sweetener in Diet Coke). In turn, your weight loss progress might be slowed.
You can absolutely drink a soup or have a small smoothie during prolonged fasts. If you want to extend even longer, I think it would help if you didn't have to work or be around other people that eat. Not sure, though, how applicable that is for you.
Regarding the re-feeding phase: It is crucial to very slowly increase your calories, no animal protein the first couple days, either. As described by another user, stick to vegetable broth, veggies, low fat yoghurt, fruits. It helps to cut up the carrot or apple for instance in tiny pieces and then force yourself to eat one tiny piece after another, chewing each piece until it is purree in your moutgh (that might take you 1 hour but you will not overeat and be full). You can use spices like cinnamon, it's a natural appetite suppressant that goes well with yoghurt or fruits.
P.S. I got a good junk of information from this book I recently read on prolonged fasts https://www.amazon.com/Lessons-10-Day-Fasting-Retreat-Self-Healing-ebook/dp/B09QJ1371C/ref=zg_bsnr_4714_13/132-7682133-3191736?pd_rd_i=B09QJ1371C&psc=1
Are you eating enough during your eating window? I have been fasting for 36 hours every week for almost a year now and noticed that when I don't eat good, nutritious food the days before, or I undereat, I cannot go through with the fast or get extremely hungry. At some point the goal should be to maintain the new weight for a little bit. You need to gradually lower your set point.
You can read more on this here https://www.amazon.com/Lessons-10-Day-Fasting-Retreat-Self-Healing-ebook/dp/B09QJ1371C/ref=zg_bsnr_4714_17/132-7682133-3191736?pd_rd_i=B09QJ1371C&psc=1
I would cut the diet coke during fasts. Your weight loss will stagnate when you consume aritifical sugars because they raise insulin levels (not blood sugar but insulin levels need to remain low when you want to achieve weight loss). In addition, aspartame, the artificial sweetener in diet coke, might negatively affect your gut microbiome. This could explain th diarrhea. You also shouldn't do extended fasts more than twice a year.
I got most of my information from this book, if you are curious to read more about the topic https://www.amazon.com/Lessons-10-Day-Fasting-Retreat-Self-Healing-ebook/dp/B09QJ1371C/ref=zg_bsnr_4714_17/132-7682133-3191736?pd_rd_i=B09QJ1371C&psc=1
I might be a bit late to the discussion but I don't think you should continue with one-meal-a-day. You need to up your meals and calories. All you did by reducing your calories, was turning your metabolism down.
I wish you good luck in getting back to healthy eating habits!!
P.S. You might want to read this book. One of the lessons is on why diets don't work. https://www.amazon.com/Lessons-10-Day-Fasting-Retreat-Self-Healing-ebook/dp/B09QJ1371C/ref=zg_bsnr_4714_17/132-7682133-3191736?pd_rd_i=B09QJ1371C&psc=1
This book has a ton of research and citation for many of the things you inquire (how hormon levels change, how longevity is affected, how diseases can be prevented and in some instances cured)
According to this book, there were studies conducted in the former Soviet Union where asthma sufferers significantly benefitted from prolonged fasts. The Russian researchers Osinin and Kokosov were experts in the field of bronchial asthma and observed 10,000 patients during prolonged fasts.