I have started a new game since the launch of Beyond. I am now 100+ hours in - I have bases in several systems, I have a big freighter and a 48 slot class A hauler.
I have completed the base computer plan searches. I have started (but not yet completed) Artemis and the Atlas Path.
I have, however, not yet managed to trigger the “Expanding the Base” quest line. To the best of my memory, it used to trigger automatically whilst building base parts - but it hasn’t happened for me.
Yes. @SingularGleam is correct. At one point Apollo will want to make sure you are ready for what lay ahead and he starts you upgrading your multi-tool and expanding your base.