I work full time, and winter was my first challenge - dark mornings when I had to go and dark evenings when I came home. Chickens get up when it is light and go to roost soon after sun down, so you could get away with making sure they had food and water for the day first thing - I have to admit I put a cheap LED light in the run during the dark winter mornings so that I could see and the girls came out anyway even though it was still dark
At that point, I would do a quick poop pick of the coop so that it was clean for the rest of day and eggs didn't get soiled, and top up any bedding as needed leaving the more thorough clean for the weekends. In an evening, I'd take out the food and water (so as not to invite vermin) and do a poop pick in the run - the process probably takes me about 5-10 min each time. Then a quick furtle in the nest box for any eggs before locking them up. I built a secure run (with a roof to keep weather out) to Fort Knox standards so that they are safe from foxes while I was at work.
I decided not to go for the automatic door opener as it is not necessary, and there is a possible false sense of security - it may fail to work and either keep the chooks locked in the coop (without food or water), or shut before they go back in (one of the hens likes to loiter long after the others have gone in - she's the one telling the world it's time to roost LOL) Physically checking the run and coop every day to make sure all was well is just part of the routine - also an opportunity to make sure the girls are fine, no injuries (especially from pecking) or illness, or signs of some infestation (mites or lice)
As for egg numbers, my 4 hybrids lay about 26 eggs a week but they are only a year old and I expect numbers to drop as they get older. Also, they did well to lay throughout their first winter but next winter I will most likely find they'll stop altogether.