Since you nerded out on this enough to do the math, you might actually be interested in this video. The only real bottlenecks to getting to these numbers are first, power and second the elevator conundrum. Solve for those and you can have quite a substantial population. Go big enough and the only bottleneck, if you want to stay a single planet species, becomes black body radiation. Check it out

Archologies - Isaac Arther (28:43) https://www.youtube.com/watch?v=TqKQ94DtS54&vl=en