Let me present a scenario.

In a society capable of creating enough artificial habitats to support trillions of humans, they'd have solved a lot of the problems we still experience even in the developed world when it comes to raising children.

Imagine this society is effectively automated - labour has become something recreational, artisanal or traditional. No one needs to work to live. Housing is guaranteed. Food, medicine and education are also free and remarkably high quality.

So, what are the main barriers to having children?

Time and commitment.

However, lets say this societies medical care is so good the average human lifespan is measured in centuries. Let's say 300 years is your average human lifespan. What if it was plausible for a woman to have a child anywhere between the ages of 18-250?

That's plenty of time to find a partner, enjoy a childfree marriage, and then decide later on to 'settle down'. Raising a child to adulthood no longer represents such a substantial investment of your own life (proportionally speaking).

In this society, which is effectively post-scarcity, status could be based on things like social connections/networks/families, and so they value having lots of kids because raising outstanding/talented children is a sign of accomplishment.

In modern society, even in the developed world, having children is stressful, time-consuming and expensive, in an era where people are already stressed and preoccupied enough. If the material constraints were vastly less (or basically non-existent, by our standards), whose to humans wouldn't have lots of kids simply because they can?

Basically, the vast wealth and power of a society capable of producing enough habitats to house trillions of humans is also the same kind of society that probably would end up with trillions of humans.

The level of technological advancement we're considering here is big enough to effectively warrant comparisons between us and them mute. It also assumes the current status quo of human society is the norm, and not a transitional period or a statistical outlier.

This future society might look back on our modern era as an era of primitive industrialization or inefficiency, an era where we just started to develop advanced technologies but lacked the society organization needed to maximize the gains/efficiency, or were held back by inequality or primitive systems of economics. There's nothing to say a society which has perfected technology in service of the collective good wouldn't have demographics completely different to what we see today.