It is possible to assemble the mission in orbit. But this will require two launch sites and multiple rockets.
I also think this is economically more feasible than the super heavy launchers. Especially if you use reusable rockets.
Do you need a super heavy carrier? I believe that for flights to the Moon and Mars, it is possible to assemble a starship in orbit and deliver a payload to it by launching heavy rockets.
For moon you don't, but for Mars you have to.
In case of China, mars manned mission is to be assembled in orbit with
7 CZ-9 launches. How many launches would there be if it is anything smaller, falcon heavy or CZ-10?
The yellow colored modules are most likely launched by CZ-9, and multiple times. The transfer modules (LEO LMO) are over 120t to 180t even when empty. And they are nuclear propulsions, you can't ask astranaut to assemble them in orbit from smaller pieces. The total mass departing from LEO is 328+246+100, about 674t.
The US would have to do the same thing that is neclear propulsion. That is why both Ares V and Starship was/is aiming at 200t LEO, even SLS block II is aiming at 180t.
BTW, in mars mission, starship will have to be in expanded mode if US goes with nuclear and keep down the launches. If they go full chemical the total mass departing LEO would be over many thousand tons, and if starship goes reusable mode, there will probably 50 launches. Sending that many thousand-tons complex to mars is like catapulting a soft tofu, think about how much structural challenge and how low the permissible acceleration would be, therefor how long time the journey would be.