### 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)

filters.clear();
	update_filters();
	invalidate();
}
void FileDialog::add_filter(const String &p_filter, const String &p_description) {
	ERR_FAIL_COND_MSG(p_filter.begins_with("."), "Filter must be \"filename.extension\", can't start with dot.");
	if (p_description.is_empty()) {
		filters.push_back(p_filter);
	} else {
		filters.push_back(vformat("%s ; %s", p_filter, p_description));
	}
	update_filters();
	invalidate();
}
void FileDialog::set_filters(const Vector<String> &p_filters) {
	if (filters == p_filters) {
		return;
	}
	filters = p_filters;
	update_filters();
	invalidate();
}
Vector<String> FileDialog::get_filters() const {