### 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)

return filters;
}
String FileDialog::get_current_dir() const {
	return dir->get_text();
}
String FileDialog::get_current_file() const {
	return file->get_text();
}
String FileDialog::get_current_path() const {
	return dir->get_text().path_join(file->get_text());
}
void FileDialog::set_current_dir(const String &p_dir) {
	_change_dir(p_dir);
	_push_history();
}
void FileDialog::set_current_file(const String &p_file) {
	if (file->get_text() == p_file) {
		return;
	}
	file->set_text(p_file);
	update_dir();
	invalidate();
	_focus_file_text();
}
void FileDialog::set_current_path(const String &p_path) {