Stiff but short daily commute leading to "heavy" legs
How hard do you ride? If you ride hard and in hard gears it could be that your legs are accumulating fatigue and simply don’t have enough time to recover from one day to the next even though it’s only 3km. It’s made worse because you don’t have an easy start to warm up.

Even pro riders don’t do hard training every day, most of the training is spent at an easy “endurance” pace.

Take it easy (at least every second day or so) to allow your legs to recover and get stronger. Get easier gears if you don’t have them.