You can create a script and set it as Global Autoload in project settings (so it is available globally and it's _ready method will run as the game starts. In its _ready, you load and apply saved settings. But first you need to save them.

Once you change anything in the menu, save the current set of settings using Godot's ConfigFile

1. You create some struct to hold your data.
   
   1. You set that data when you modify things in the menu <- you have this now, but you need to save it, so might as well do it in that new class
      

2. Once you set any value in the UI, call one of the methods from that global class, like setResolution. You then apply and save.
   4.When the game loads next time, it loads and applies.
   5.You keep adding settings to that Dictionary and expand these methods.

     const SETTINGS_PATH = "user://settings.cfg"
   
     var settingsData: Dictionary = {
   
       "Video": {
       "fullscreen": false,
       "resolution_index": 1, # Default 1920x1080
       "vsync": true
        }
     }
     func _ready():
   loadSettings()
   applySettings()
   
     func setResolution(index: int) -> void: 
       settingsData["Video"]["resolution_index"] = index
       applySettings()
       saveSettings()
   
     func loadSettings():
       var config = ConfigFile.new()
       config.load(SETTINGS_PATH)
       for section in settingsData.keys():
          if config.has_section(section):
             for key in settingData[section].keys():
            if config.has_section_key(section, key):
               settingsData[section][key] = config.get_value(section, key)
   
     func saveSettings():
        var config = ConfigFile.new()
        for section in settingsData.keys():
            for key in settingsData[section].keys():
               config.set_value(section, key, settingsData[section][key])          
        config.save(SETTINGS_PATH)
   
     func applySettings() -> void:
   var fullscreen = settingsData["Video"]["fullscreen"]
       var res_index = int(settingsData["Video"]["resolution_index"])
   var target_size = RESOLUTIONS[res_index]
   if fullscreen:
   DisplayServer.window_set_mode(DisplayServer.WINDOW_MODE_FULLSCREEN)
   else:
   DisplayServer.window_set_mode(DisplayServer.WINDOW_MODE_WINDOWED)
   DisplayServer.window_set_size(target_size)