Yes, I still have to look up libraries for, eg pip, and I haven't gotten to the level of knowing every compiler error yet.
But it is very much a doable goal. Especially given that knowledge transfers between languages and libraries. Once you learn the thought process of the dev who wrote it, you can guess how they did or are going to do everything after that, creating a short cut where you can guess and usually always guess the right answer. It's much quicker than using SO.
Is this because this Web programming innately needs lots of tools, etc. to work, or because the modern programming ecosystem (including stack overflow) has allowed it to grow to be this way?
Just to nitpick a bit, I would say that complexity grows quadratically - proportionally to the number of potential interactions between subcomponents.
I have a hard time getting into a flow state when I'm looking something up, but when I know the language inside and out it's easy for me to get into a flow state.
So much so, when I learn a language I try to know it well enough to never have to google for help. Of course, I still google around at times, but I find the less I have to the happier my day is.
SO is a blessing, but it's also a curse. Younger devs have no idea what they're missing out on.