Anonymity isn't a thing you 'achieve' anymore than you obtain 'health' by switching to kale twice a week.
GOS, like kale, is just a step in a right direction.
Beyond that, it's a matter of degree. More anonymity typically costs you. (more effort, inconvenience/sacrifice, etc.).
What specifically is your goal? What steps have you alreasy taken? Are you wanting to stay private from your ex, or just dislike the direction big tech is going? How and for what do you use internet? Are you on social media? Do you use email aliasing? There are thousands of questions that could be asked that go beyond which tab you tap on your rectangle.
That said, Bazzel's book 'Extreme Privacy' is quite a deep dive that covers many pertinent aspects.