Just a quick message in regards to human population in the galaxy of ED:
It only takes a few minutes to go to eddb, sort by population and copy the highest 1350 entries (27 pages on eddb) into a spreadsheet and add up. The very last entries are just shy of under 1 billion (( 965,583,014 to be exact )). The total amount of these 1350 systems is: 5,811,648,873,213 which makes the original 6+ trillion on the 2nd page sound like an accurate assessment.
Also, to think that birthrates would decline overall in a galaxy is basically totally free to colonize (no need for planets, just build a station) is very limited, terrestrial thinking. It's not a far stretch to say that you want to make as many offspring as you can to strengthen your claim and proliferation on many a station. This is not me justifying BGS logic onto the fictional world logic, this is just mere assessment of our own history. When lands are for the taking, there is always a boom in birthrates, because workers and soldiers were needed. 1300 years from now with medicine where it is and the upper echelons of society live northwards of 150 years, that could mean (I'm taking wild guesses here, the lore experts should please correct me on that) that you can do your job for longer. I wouldn't be surprised if the average lifespan is about 100, making your average retirement age 85. If such a thing as retirmenet still exists in the far future.
With all the hazards of space, sun radiation poisoning of prolongued flights, living in inhospicable stations or planetary settlements and outposts without a breathable atmosphere, plus the constant warmachine and the countless death toll it takes, it's almost ridiculous to insinuate that there is any incentive to curb birthrates. Especially if it is so easy to just travel to the next system. Making colonies and stations is no longer a matter of "if" and "how". It's a matter of "when". If a suitable claim that is profitable can be staked, it will be done.