Upon further testing, I found out that it's probably caused by the the fact, that the colony ship was captured via Boarding Crew component from Pirates. Because when I tried to colonize the planet with Colony Seed Nanites or with newly constructed colony ship it's working as should without any shenanigans as on the video in my initial post.
I also found out when searching this forum with specific words related to the capturing the enemy colony ship, that this is also a known issue.
I guess, this thread can be locked/deleted then.
I will try to be more thorough with my own testing and checking the already reported bugs next time. And if anyone spent any time checking this, needlessly, my apologies.