Indeed, is this low rate, compared to 67.4 km/sec/Mpc or 72 km/sec/Mpc, due to the role of dark energy?
We have a special way of looking at this question. In short, dark matter is produced by black holes and stars, and it contributes to the expansion of the fabric of space. So the rate of expansion is not the same in all regions of space, and it is not the same in all time periods. It depends on the density of the contributing stars and black holes at that time and in that region.
See https://www.researchgate.net/publication/383125125_Towards_the_Theory_of_Everything_Step_1_-The_Photon
I think that the expansion rate in the early@ universe is c and c is also the expansion rate today.
Yes, dark energy is to play the roll for the expansion of the universe.
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