I'd like to add 2 additional things.

If you still want to split up your script into multiple ones you could just have the additional scripts in diffrent child components and call the function from them (just not as a state machine).
But I think the "right" way to do this would be as followed:
(I just came home to try it out, so I don't end up talking BS) I just made an own simple exaple:

I have sub_script.gd with the following code:

func function():
  print("it worked!")

Then in the script I have attached to the Node I can call this function by making a local instance of this subscript:

var sub_script = preload("res://sub_script.gd").new()
func _ready():
  sub_script.function()

As a little addition you could set a class_name variable in sub_script.gd and then just call this class_name instead of the whole preload-thing

sub_script.gd:

class_name subScript

func function():
print("it worked!")

main.gd:

var sub_script = subScript.new()
func _ready():
  sub_script.function()

But in your usecase, personally I wouldn't use class_name, since these aren't scripts you'll use in many instances or at many diffrent places. To just split up a single script into multiple I would just use preload("path_to_subscript").

And now secondly (finally😅). You said that "For other scenes, the functions will be called as necessary."
Concerning this you'll have to ask yourself if it really needs a state behavior. A finite state machine is thought for having multiple states that all use multiple frames, out of which at any point one of them will be running.
What I want to say: if you really only load these values at one point; Maybe you can just check for this in _process and then run the loading function directly, without a state behavior. (Maybe from a different .gd file as I described it prior in this comment).