I took a look at your project in the editor and it appears you have two problems.
First, you should load the file if it exists and update the GUI when the scene starts:
# Call this function at the end of _ready()
func _load():
var file = File.new()
var filename = "user://saved_game.sav"
if file.file_exists(filename):
file.open(filename, File.READ)
fruits.parse_json(file.get_line())
_update_gui()
func _update_gui():
get_node("lbl_orange").set_text("Orange: " + str(fruits.orange))
get_node("lbl_lemon").set_text("Lemon: " + str(fruits.lemon))
get_node("lbl_pear").set_text("Pear: " + str(fruits.pear))
The second problem is that you are trying to save variables from the second scene in the same file, as if it had no awareness of the other scene.
You have two options:
1) The other scene can do the same thing but have a different file. This is the simplest given your situation.
2) Always save and load the whole data
3) Keep the same unique file and navigate into it.
I personally use 2) if the file is reasonably small, but because your scenes don't access each other you cannot do it directly, unless you have a singleton holding the variables.
If you want 3), you get a third problem:
How could you recognize which line belongs to which scene in the file?
Well, this is a bit tedious to do with the current API, so that's why I do 2).
If you really want that, a possible way is to read the file first as a dictionary, modify a part of this dictionary, and save it back. But that's not much different from saving/loading everything.
Edit: Warning, the following is a bit more advanced and IMO should be only relevant for big files.
It's a bit easier to do 3) by saving binary data rather than JSON.
Knowing that you have 3 integers to save for each scene, you can save them as 16-bit integers (2 bytes each) with File.store_16(). So using File.seek() you can jump directly to the data you want to read, and read only that without having to parse everything in JSON. So for example, fruits would be in 0, and vegetables in 6 (because 2bytes * 3 = 6).
# Fruits scene
file.store_16(fruits.orange) # Each call to store_16 advances the cursor by 2 bytes
file.store_16(fruits.lemon)
file.store_16(fruits.pear)
# In Vegetables scene, start after vegetables
file.seek(6)
file.store_16(fruits.carrot)
file.store_16(fruits.tomato)
file.store_16(fruits.potato)
# Note: I used store_16 but you could use 8 or 32, it depends what
# is the maximum value you want to store (max 16-bit value is 65536)
Same for loading, you would jump to the correct position and read values with File.get_16() in the same order.