Well, the kata has no random tests, so...

Sample tests puts assumption on how TimeLinesState should be defined. The initial code has signature

data TimeLinesState s a = TimeLinesState {}

but sample tests can only be run with

data TimeLinesState s a = TimeLinesState {runTimeLinesState :: ... }

, which this is not specified anywhere, and is basically a fake degree of freedom.

The initial code is a mess. Shouldn't instance Applicative be defined before instance Monad? And the type hints can (and should) go to the initial code instead of the description.

Is the number of channels hardcoded as 2? Or is "multiple" to be taken as "unlimited" ?

The example where the state type is the same as the output type is less than ideal to clarify this.

Needs actual specs instead of just an example. Again, autor, this is an invitation to read your mind.

Needs actual specs. Examples are nice, but they are an invitation to read author's mind. Please specify how branchTimeLines is supposed to behave.

get, put, modify, state and gets also need actual specification. You can assume the normal behaviour is known, but their behaviour with multiple timelines is not.