### Godot version

v4.1.stable.official [970459615]

### System information

Windows 10

### Issue description

When changing the `file_mode` of `FileDialog` from "Open File" to "Save File" via code the "Save" button keeps disabled until a file or folder is selected if the "Open" button was disabled before.

Basically the button activity has to be updated when `file_mode` is changed. I have made the change already but the last time I opened an PR without an issue some people requested I open one. So here you are!

### Steps to reproduce

- Open the MRP and start it
- click anywere to open the dialog
- after 10 seconds the dialog changes file_mode
- if the button is disabled before the change it is as well after it

### Minimal reproduction project

[file_dialogue_test.zip](https://github.com/godotengine/godot/files/11991311/file_dialogue_test.zip)

int idx = filter->get_selected() - 1;
	if ((idx == -1 && filter->get_item_count() == 2) || (filter->get_item_count() > 2 && idx >= 0 && idx < filter->get_item_count() - 2)) {
		if (idx == -1) {
			idx += 1;
		}
		String filter_str = filters[idx];
		String file_str = file->get_text();
		String base_name = file_str.get_basename();
		Vector<String> filter_substr = filter_str.split(";");
		if (filter_substr.size() >= 2) {
			file_str = base_name + "." + filter_substr[0].strip_edges().get_extension().to_lower();
		} else {
			file_str = base_name + "." + filter_str.strip_edges().get_extension().to_lower();
		}
		file->set_text(file_str);
	}
}
void FileDialog::update_file_list() {