### 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)

_change_dir("..");
	_push_history();
}
void FileDialog::_go_back() {
	if (local_history_pos <= 0) {
		return;
	}
	local_history_pos--;
	_change_dir(local_history[local_history_pos]);
	dir_prev->set_disabled(local_history_pos == 0);
	dir_next->set_disabled(local_history_pos == local_history.size() - 1);
}
void FileDialog::_go_forward() {
	if (local_history_pos >= local_history.size() - 1) {
		return;
	}
	local_history_pos++;
	_change_dir(local_history[local_history_pos]);
	dir_prev->set_disabled(local_history_pos == 0);
	dir_next->set_disabled(local_history_pos == local_history.size() - 1);
}
void FileDialog::deselect_all() {