I went into a old save of the second game again and have to correct myself: The total ships count of all four shipping lines together was actually 800+ on my side (seperating in 560-280-few-few), not the biggest already, so much fewer are needed for problems. Also, when I take the Precursors, Invaders, and the Star Swarm out, only 5 NPR races remain. Altogether they own a mere 232 civilian ships, which is nothing compared to mine, so in this game the slowdown must instead come prominently from the players side. This is likely so though, because I started the game with a difficulty modifier of 20% so the other races all fall back alot.
(I still had to learn many things since in my first game I lost pretty early to BUG-class bombardement missiles with only ever having had one real military vessel flying, and knowing nothing about many functions)
In this game I only owned 3 other systems, only one of which colonized for real, and the other two remote mining grounds, and all in 1-2 jumps range of Sol. Nothing against the wide spread expansion I manage in my third game right now and without problems.
I cannot name the point where the game became impossible to manage anymore though. It is like watching a plant growing. It happens unnoticable slowly every turn, and at some point you just look back and recognize - things have changed. I was in denial for quite a bit longer than it was good for me, not wanting to give up on the game I had already invested many hours in. At this end save I myself can see 86 systems, and when I switch to the only other selectable race (which is one which i am allied with) then I see 46 system, where some likely are discovered by me too. ..But there must be quite a bit more with the other 3 hidden races, so who knows.
One could make an experimental game though, where a good number of starting npr are present, and the empires all start with boosted population. One could cheatingly fund their shipping lines to start the sprawl as early as possible, so we have many civilians even when few systems are discovered, and then see how and when it really becomes a problem. Maybe define a line of 'unbearableness' that when a 1-day turn takes more than 20-seconds or 30 or so, the game is classified as broken, and the census about civilian ships and systems can be made.