Well, Distant worlds matches almost all this:
- the game is so heavy that every task can be automated (or not) to help the player. Colony taxes, mining stations building, ship design, ground forces recruitment and much more.
The ships can be designed as you like, basically you're piling up the components you want according to what is available with your tech level and what you would like your ship to do.
- you can almost customize everything at game start: size and shape of the galaxy (up to 1400 star systems, REAL star systems, not some arcadish thing with a single planet alone in the dark like in some games), amount of pirates, development level of your opponents, victory conditions, tech levels, tech research speed, availability of colonizable worlds and independant colonies, storylines etc ...
- it is SP only (too complex to really work well in multiplayer anyway)
- about the approaches, well the victory conditions (specific to each race) and the start settings can help having completely different games but IMO there's no real way to win, for exemple with pure diplomacy, without fighting.
- modding isn't very developped for now, it's supposed to be favoured in a forthcoming expansion.
- That's definitively one of the most realistic games I've seen on many subjects. For example the economy is simulated and independent. There's a lot of ressources required for ship/station building, harvested at the colonies or in space using mines, then shipped to where it is needed by private freighters, prices vary according to availability and demand, there can be shortages.
The only things you control about the private sector are the transport ships/mining stations designs and the amounts of taxes.
Well, there's really a lot to say about this game. The best is that you google it and find a few tests, it is very good but it's wise to have a better idea of what it is before investing such price.
Oh, one more important thing, some Death Stars can be found in this game, you might even build your owns if you're advanced enough and very lucky.