### Godot version

v4.0.beta10.official [d0398f62f]

### System information

Windows 11

### Issue description

Using a custom "Project Settings Override" file causes Godot to immediately modify main project file (`.godot`) on startup.

The attached project demonstrates this issue. The project has the following 3 things defined:

1. Window display mode is set to "Exclusive Fullscreen" (`window/size/mode=4`) in main project file.
2. Custom project override file is set to "res://override.cfg" (`config/project_settings_override`).
3. Inside "res://override.cfg" window display mode is set to "Windowed" (`window/size/mode=0`).

Opening this project will immediately modify main project file to have "Windowed" display mode (discarding original "Exclusive Fullscreen" setting).

### Steps to reproduce

1. Open example project.
2. Go to Project Settings -> Display -> Window -> Mode.
3. Expected option is "Exclusive Fullscreen", actual result is "Windowed".

### Minimal reproduction project

[override-issue.zip](https://github.com/godotengine/godot/files/10312624/override-issue.zip)

ERR_FAIL_COND_MSG(!props.has(p_name), "Request for nonexistent project setting: " + p_name + ".");
	
	props[p_name].initial = p_value.duplicate();
}
void ProjectSettings::set_restart_if_changed(const String &p_name, bool p_restart) {
	ERR_FAIL_COND_MSG(!props.has(p_name), "Request for nonexistent project setting: " + p_name + ".");
	props[p_name].restart_if_changed = p_restart;
}
void ProjectSettings::set_as_basic(const String &p_name, bool p_basic) {
	ERR_FAIL_COND_MSG(!props.has(p_name), "Request for nonexistent project setting: " + p_name + ".");
	props[p_name].basic = p_basic;
}
void ProjectSettings::set_as_internal(const String &p_name, bool p_internal) {
	ERR_FAIL_COND_MSG(!props.has(p_name), "Request for nonexistent project setting: " + p_name + ".");
	props[p_name].internal = p_internal;
}
void ProjectSettings::set_ignore_value_in_docs(const String &p_name, bool p_ignore) {