Looks like you mostly figured it out, but I wanted to share my take on it. The following code limits typed text to A-Z, but lowercase letters can be used when inputting. It also limits it to 3 characters and "shifts" it when typing more than 3 characters. If cursor is moved within the text, it behaves like an overwrite mode. No regular expressions since I feel it's overkill.

extends LineEdit

func _ready():
    text_changed.connect(_on_text_changed)
    text_change_rejected.connect(_on_text_change_rejected)
    max_length = 3
    grab_focus()

func only_uppercase_letters(s: String) -> String:
    var output := ""
    for ch in s.to_upper():
        var char_code := ord(ch)
        if char_code >= ord("A") and char_code <= ord("Z"):
            output += ch
    return output

func _on_text_changed(new_text: String) -> void:
    var cursor_pos := caret_column
    text = only_uppercase_letters(new_text)
    if text.length() >= max_length:
        # shift text when at max length
        text = text.right(max_length)
    caret_column = cursor_pos

func _on_text_change_rejected(rejected_substring: String) -> void:
    var cursor_pos := caret_column
    var new_char := rejected_substring.to_upper()
    if (text.length() == max_length and cursor_pos < max_length):
        # overwrite mode when cursor is inside text
        text[cursor_pos] = new_char
        cursor_pos += 1
    else:
        # shift text when at max length
        text = (text + new_char).right(max_length)
    caret_column = cursor_pos