Do I need to say it as well? Mudguards. Proper ones, not clip on pseudo-guards.
I work contracts in different places, anything from 6 months to over 2 years at a location, and commute all year round. Currently I have a very short commute, so I just ride in my work clothes. Waterproof jacket and trousers go over the top if it is raining.
For longer commutes that involve a proper cycle, I take a set a clothes in on Monday, leave the trousers at work, and then just take shirt/socks/pants/towel each day. If you can hang up a towel to dry properly, then you can just take one in on Monday each week. Usually I can't do this, so I just take a small microfibre towel in the pannier each day (cheapo Aldi ones). Shoes are carried in the pannier at the start of the contract, stay at work for the duration, and only come home at the end of the contract. Ditto for my bike lock, unless I need it to pop into the shops on the way home occasionally.
Carrying clothes - shirt and trousers are just folded up and carried in my pannier.
Food - just do whatever you normally do. If you take in sandwiches, just stick them in the pannier. You may be eating a bit more if you are not currently doing 20 miles a day.
Weather - wear whatever you normally wear for cycling. My waterproof jacket travels in the pannier all year round, and the rest varies between shorts and jersey in summer to bib longs, thermal jacket, overshoes, Buffs and winter gloves with liners when it gets really cold in winter.
I know you have said you don't like stuff on the bike, but a rack and pannier beats a rucksack hands down for regular commuting. I can comfortably carry all the gear described above, and if I decide to do some shopping on the way home, I can pile a good load of stuff in an unrolled pannier. Carrying any significant amount of stuff on your back in a rucksack isn't very nice for cycling.