A few thoughts.
As I'm demo-ing the kitchen, also starting to think about putting the new one in. IE, what order do I need to do?
Tasks:
Demo
A good place for actual construction to start, but miles of planning comes first. I know it a technicality and it seems like you have started and are doing that, but I always like to have it (usually in multiple steps/phases) on my check list.
Electrical - rewire to code, new lighting, etc
In most places existing wiring is grandfathered. So unless you are changing it, you might not have to bring it up to code.
I have some electrical running and other utilities/systems running in the toe kick space of a couple of my cabinets so I had to do some after/with cabinets.
Repair wall as needed
Paint wall/ceiling
Just be prepared for touch-up. It is far from impossible that there will be a ding/scratch/scrape/scuff. Also paint is more durable if given time to cure.
Cabinets
As mentioned backsplash is missing from the list and I would add exhaust hood/over-the-range microwave at this step as well.
Plumbing - not moving, just connect/fix the broken shutoff valve and unclog the drain.
This depends on where the valves our and whether you have additional shut-offs without taking the whole house offline. If the valves will be located in a cabinet you may have to remove them before installation of the new cabinets, or before removal of the old, in order to keep the holes in the cabinet back/bottom small. If you cannot shut off individual runs you can buy sharkbite caps and the removal tool for later.
Personally, I like to address all of the utility first. That way if I find a problem, or cause a problem/leak, I do damage or have to undo work. So I would have plumbing be two steps. The first would be up with demo and electrical addressing all of the removal of old items, and fixing of existing problems, and the second somewhere after cabinets and countertops which addresses new valves and final connections (also you cannot install and connects sinks/faucets until the countertops are in).
Flooring (sheet laminate)
In a complete remodel, I like to do flooring before cabinets. That way I can run the flooring at least slightly under the cabinet and avoid all the work of fitting it tight to the cabinet or using a (in my opinion) ugly solution to cover any gap.
Appliances
This one depends. I have put appliances in earlier because I wanted to be able to use them sooner. I have also put appliance is with the cabinets only partially installed for ease of access (shouldn't be impossible with the cabinets installed, but sometimes easier.
Is that in order?
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Missing from the original post, though discussed in the thread is countertops. If you are going solid surface a fabricator can quote the job using basic measurements, but should come out and measure everything and address out of square or uneven walls. There are DIY friendly countertops out there in which case measurements will be more critical. Countertops were the only thing we hired out in our kitchen ... we even build the cabinet and all 29 drawers they contain from scratch. This probably slots in between where you have cabinets and plumbing.