If you use
_input, then testing if there is no input is actually up to you.
As I said:
Testing if there is no input doesn't make sense on its own, IMO. Your game reacts to input by setting some variables and calling functions, so you should be able to check your own logic variables and do something in consequence (and if you don't have some, create them, the boolean I mentionned above could be one, but I'm sure you have something like "direction", "is jumping" or "is moving" or whatever your game does).
As an example, considering only one input:
move_local_x(-speed * delta)
# Moving every frame
# Not moving, we are idle here (but called every frame so be careful)
moving_left = true
# We are going to move now, begin animation
moving_left = false
# We are idle now (called only once because we are in _input)
Note that you are not forced to do the idle animation directly in
_fixed_process, these are just starting points, especially if you have more than just one input.