My kids are younger (4 & 7) , but I also have this problem.
I think you need to have a sit down with your 14 yo and explain how unwell you are and how he can best help you. Tell him what is expected of him and agree with what he can take ownership of and what he still needs help with, what he is going to work towards doing himself etc. And a timeframe of when he should be doing it.
eg. Get his lunch box, water bottle, jumper ready in the morning, do his homework when he gets in, prepare his school bag before bed etc.
Write everything that he should be doing every day down on a tick list (i have these tick lists for my kids https://www.amazon.co.uk/dp/B0CRBDHFXS/)
Timers are also good for keeping focus. Rather than constantly saying "we've got 20 minutes, we've got 10 minutes, 5 minutes, we should've left by now!" You can get big timers that count down which are useful as it becomes more visual if he can see the time ticking away from him. You could also try them for homework "you don't have to spend hours on this, just get as much of this done as you can in the next 20 minutes". He might be surprised at how much he can do when he isn't spending an hour whinging about it!
Don't know what the distractions are before leaving the house, but try to reduce/eliminate as much as you can. Eg. No tv or phones before everyone is ready, school bags packed the night before, clean uniform out on a chair before bed so there is no scrabling around looking for a clean shirt etc, look at which breakfasts take the quickest amount of time (eg.my kids take longer eating cereal than toast as they end up keeping topping up the bowl as they eat so it almost never empties!).
I would also look at your own routines. One thing I find about being a parent is that I need some time to myself of an evening, and sometimes I stay up far later than I should, just because I need some time to myself which isn't spent working, parenting, or doing housework. But the later I stay up, the more grumpy, stressed and short tempered I am the next day, whixh then affects the kids moods too. So, if it is possible, try to get a few more early nights and a bit more sleep if you can. Appreciate this is easier said than done though!