Breaking fasts with cooked foods is to lessen the fallout from ending a fast too soon, at least that's the theory behind it- I've never tested it myself. Stewed fruits are less cleansing than raw fruits and stewed veggies even less again, this isn't actually bad for us but it's a bit over cautious I think. It just seems like there's more substance to it because it is closer to the way we normally eat. The whole point of needing to fast is that the way we normally eat isn't healthy for us though so I'd rather stick to raw.
I do think that for fasts of up to 2-3 weeks at least you do need at least a couple of weeks to recover from them. Beyond that the refeeding period may be able to be shortened but again it comes down to listening to the needs of your body. That first week is all about allowing your digestion system to slowly come back online (sorry been watching a lot of sci-fi lately hence the terminology) as it needs to adjust again just as it does at the beginning of the fast to ketosis again. The main safety thing is not to overload it with too much food, low water content food, or unnaturally highly concentrated foods. Beyond that safety aspect the body is also seeking to replenish vital nutrients lost during the fast and will want high quality foods to restock from. The best thing for all these purposes is raw fruits. Also ketones continue to be produced for the first week after a fast and I think that it is important to allow the body time to use them between eating for that first week and use the most quickly digested foods which are again fruits.
I do think it's best after an extended fast to not introduce full normal sized meals until the second week after the end of the fast for these reasons. And then continue on through the second week still eating raw foods and each day just adding a single cooked or processed food to my salads. I've done it this way and felt like I've received the full benefit of the fast by doing just that.
Coconut milk should be okay. I've always been a bit suspicious of the tinned stuff because it says nothing added but what is inside is nothing like what I find when I cut open a conconut myself! lol So I'm not really sure how they process it to make it like that. I would probably research it first before using it as part of refeeding if you are thinking about the prepackaged stuff. If you do let me know. :)