Suppose I have a function (in Kotlin over Java):
fun <E> myFun() = ...
where E is a general type I know nothing about. Can I determine within this function whether there exists an extension function E.extFun()? And if so, how?
I very much doubt this is possible.
Note that extension functions are resolved statically, at compile time.
And that they're dependent on the extension function being in scope, usually via a relevant import. In particular, it's possible to have more than one extension function with the same name for the same class, as long as they're defined in different places; the one that's in scope will get called.
Within your function, you won't have access to any of that context. So even if you use reflection (which is the usual, and much-abused, ‘get out of jail free card’ for this sort of issue), you still won't be able to find the relevant extension function(s). (Not unless you have prior knowledge of where they might be defined — but in that case, you can probably use that knowledge to come up with a better approach.)
So while I can't say for certain, it seems highly unlikely.
Why do you want to determine this? What are you trying to achieve by it?