My latest 1.12 save has around 18bn humans across 20 populated systems and around 5bn aliens across a small subset of those systems.
I have around 200+ 5k ton frigates, 6 60k ton BBs, 4 45k ton BCs, 2 70k ton CVs, 4 30k ton CVLs, around 100 or so DDs, 40 CLs, 2 CGs and 8 CA/CSs. It obviously could be a much bigger fleet but the only part I'm really constantly expanding are the frigate and destroyer patrols to defend the large amount of space my empire takes. However, the larger offensive elements will also be expanding since I take a very modular approach to my empire, with each administrative sector having complete self-sufficiency with mines, shipyards, refineries and both defensive and offensive fleets.
But I think this is the largest population count I've ever reached in any Aurora game.