Readable and efficient code?

Pretty sure you can just combine the cases where modulo result is non-zero and drive your worker text from the 'remainder' variable. Something like (untested):

var worker_num = 6
func _on_Button_pressed():
    var input_number = get_node("../LineEdit").text.to_int() #assuming your not reusing you can chain .to_int()
    var pieces_per_person = input_number / worker_num
    var remainder = input_number % worker_num
    # following bit looked to be the same under all conditions
    var base_txt = str("PIECES   ", input_number)  + "\n" + str("PIECES PER PERSON   ", pieces_per_person) + "\n" + str("REMAINDER   ", remainder) + "\n"
	
    if remainder == 0:
	get_node("../Label").set_text(str(base_txt + str("All Workers   ", pieces_per_person)))
    else:
        # use remainder and worker_num - remainder to drive text for else conditions. 
        get_node("../Label").set_text(base_txt + str(remainder, " Workers   ", pieces_per_person + 1)  + "\n" + str(worker_num - remainder, " Workers   ", pieces_per_person))

Added a small tweak, replacing the hard coded number 6 with a var worker_count makes this approach reusable for any other worker counts. Though would expect this to live outside the button pressed function if it was going to change programmatically.

Imagine the type casting above is iffy, but other than that think it should work.

In addition, place this before the function:
onready var label: Label = get_node("../Label")

Then use label in place of get_node("../Label").

DanchoLudiq And how should I go about Localization option for PIECES, PIECES PER PERSON, REMAINDER etc if I want to have it in two languages?

Feel the right answer is to spend some time looking over https://docs.godotengine.org/en/stable/tutorials/i18n/internationalizing_games.html as at a glance there is a better way than the bootleg approach I thought of below, which was:

I would probably use a dict with my primary language as keys for readability, with the lang_choice variable in a global singleton. Something like this:

var lang_choice = "en" 
var localiser = {
	"PIECES":{
		"en": "PIECES   ",
		"fr": "PIÈCES   "
		},
	"PIECES PER PERSON":{
		"en":"PIECES PER PERSON   ",
		"fr":"PIÈCES PAR PERSONNE   ",
		},
	"REMAINDER":{
		"en":"REMAINDER   ",
		"fr":"RESTE   ",
		}
}

var base_txt = str(localiser["PIECES"][lang_choice], input_number)  + "\n" + str(localiser["PIECES PER PERSON"][lang_choice], pieces_per_person) + "\n" + str(localiser["REMAINDER"][lang_choice]), remainder + "\n"

Edit: This feels like it would get cumbersome/messy quickly, but surprisingly my bootleg approach is not far off what is recommended here: https://docs.godotengine.org/en/stable/tutorials/assets_pipeline/importing_translations.html#doc-importing-translations
Seems like translations in general is just a massive hassle lol.

DanchoLudiq Can you explain how this .replace thing is working please?

SO the docs are here: https://docs.godotengine.org/en/stable/classes/class_string.html#class-string-method-replace

But to give some context I will use a simpler example:

"This is a string".replace("string", "word") = "This is a word"

So the '.replace' function acts on the string object to the left of it, replacing the instances of the first parameter passed to it (in this case "string") with the second parameter ("word") as a new string object.

In my example I used the fact the output is also a string object to chain multiple replaces together, e.g:

"This is a string".replace("string", "word").replace("word","book") = "This is a book"

I account for when things like "1 workers" should be "1 worker" or when a line is redundant I replace it with "" but I do it all in one command (which is ugly). This replaces the IF block entirely as in most cases the output is the same, and predictable when not. It is probably confusing because I am not just passing a typed string as parameters to replace, but rather programmatically defined strings.

Like I said this is foul/not readable and I would not recommend it unless it quantifiably improves performance in a way that is actually necessary. I suspect it doesn't/isn't, so always favor readability first as it makes code easier to revisit down the track or if others need to review/modify it.

Format strings are an alternative.
https://docs.godotengine.org/en/stable/tutorials/scripting/gdscript/gdscript_format_string.html#gdscript-format-strings

For old-time C/C++ programmers like me, it's GDScript's version of sprintf.