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Something at the level of a loop does not strike me as something you can call a design pattern.

I agree. I'd be more inclined to call something like that an idiom.

> Functional programming still has patterns, they are just different patterns.

Yes, exactly what I meant by

> the design patterns relevant in those domains are not really called "design patterns".

I was thinking of things like algebraic or categorical laws, or invariants.

> Monads

Are "just" an interface a data type can implement/obey (in languages that support higher kinded interfaces)

> a foreach method/function for iteration over data

Again, "just" an interface a data type can implement/obey.

Patterns being reified as language objects don't make them not-patterns. Trusty old function calls are still patterns, only reified from asm routines and procedures.