Amateur question: how circuit analysis methods are applied in "complicated" circuits?
Basically for pen-and-paper analysis you break down the circuit in "logical" blocks, like in a block diagram and you mostly analyze them separately. I put that "logical" in quotes because it's not in any formal sense.

There are however fast SPICE simulators that can simulate an entire chip and these obey KCL, KVL etc. but may use somewhat simplified component models.

I should also note that breaking down circuits into simpler sub-components (as we do on paper) is also done in some software tools like HSIM. Hierarchical simulation is one of the tricks in the arsenal of fast SPICE simulators.



Regarding that SMPS schematic that was added as example: for pen-and-paper analysis you need to be familiar with the kind of circuit in question (starting with SMPS topology) and the identify the "macroblocks" like input filter, rectifier, main switcher[s], transformer, main controller IC (usually includes error amplifier), etc.