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So the correct way to punch in k1/kickboxing is to twist your body, on your foot as you do it, right? But when I try to increase my rapid punching speed I saw that I cannot twist my feet to punch quickly enough, so I just turn my body in the core.
I watched McGregor's practice videos and saw that he barely twists for rapid punches as well.
So how does it work? Is less force in the punch a cost for the number and speed of punches? Or am I just not there yet and should focus on my technique?
I think you are mixing up training purposes here.
Speed drills are mostly for three purposes: Rhythm/reaction training, muscle memory, and cardio. The latter is especially true for working the bags. Other aspects are things like footwork/angles, establishing kinetic chains crossing the corpus callosum, etc. If you are doing this fast, you can do many more moves within the same training time. And considering that internalising movement and reaction patterns perfectly takes thousands of repetitions, speed is a viable option - with limitations, see at the end of this answer.
If you look at actual boxing matches, you will notice that speedy combinations become less common, especially the heavier the opponents are. Lightweights are insanely fast, but they do not have much weight/power to put behind hits anyway, so they might as well produce power by sheer speed (momentum = mass x velocity). Fast hits are mainly used for concealing movements, changing angles and setting up more powerful strikes with mass behind them that hit their mark, i.e. to provoke reactions and put opponents under pressure. The Klitschkos (when they still were fast) used their fast jabs and superior reach to unnerve opponents and force them to open up at some point, for example.
Really dangerous are the guys that are heavy and fast. If you look at this video of young Tyson, you can see how he is insanely fast and can still generate insane amounts of power by either rotation or ducking plus upwards movement (essentially pushing from the ground up) - or even a combination of both. Any of those hits would have felled anyone but the best-trained athletes if they connected and weren't blocked. This is how he trained and fought. Compilations of his KOs will show you that most of his KOs were produced by changing from his very fast and powerful rotational hits to uppercuts, less commonly the other way round. Of course he had changes in rhythm and pressure as well - where he just tested or rested - throughout longer fights against tougher opponents. But this is high-level boxing, where a lot is depending on subtle and fast footwork and very strong and fast core and leg muscles - a level McGregor could never dream to reach in the short amount of time he had for training. I'd even suspect that Mayweather had been told to not end it too fast and back down a bit in between to give McGregor his moments - just look at how relaxed he looked, grinning into the cameras between rounds.
Looking at McGregor's fight, you may sarcastically say that he fought as he trained; he may have looked good to the eye of the usual bystander because of more or less speedy combinations and evasions, but he could never actually really put Mayweather into danger as he basically rolled Connor's strikes all the time, even if they would have been powerful - which they weren't - they wouldn't have hit him hard (exception: few uppercuts which he just ate and got on). Even if Mayweather had not rolled so many of them, they would have lacked the power to knock him out - notwithstanding the fact that even light hits stack up their effect over time. As McGregor's cardio failed, he was determined to lose even that part of making Mayweather move out of the way and looking good.
Long story short: Like in every other martial art, it is better to start slow but correct and become gradually faster without losing the precision than having speed but lacking technique. It takes more time to achieve both than McGregor had, so I suspect his coaches aimed for giving him cardio and speed so that he could stand the length of the fight (or at least more than six rounds) and put some pressure on Mayweather - hoping for the very small chance of a lucky punch. Thus, your aim should be good technique first and gradually more speed in the long term so that you do not develop "bad habits", i.e. patterns that are ineffective, but reflect your training.
