If there was no such thing as natural immunity then you would never recover from Covid to begin with, and even if you did, you would just get it instantly again. There's a reason we call this natural defense system in our body an "immune system".
Furthermore, when the term "Omicron is the vaccine" is used, it simply means that the best way to defend yourself against every person you encounter that is knowingly or unknowingly spreading Omicron is to have already had Omicron. This is not complicated stuff.
Now it would be illogical to think that because you had a prior version of Covid that you are naturally immune to any and all future variants. That's just stupid and the same logic applies to vaccines. If you've never had Covid, getting a vaccine that was engineered 2 years ago to defend against the initial versions of Covid is a great way to protect yourself against those variants, but it's not going to do you much good against future variants that have many mutations.
I stated this in a prior thread but I will state it again. I have a group of 10 - 12 friends that I regularly travel with multiple times per year. Within the span of 1 week, every single one of us got Omicron, and every person was vaccinated except for myself and my wife. There has been virtually no difference whatsoever between us all in terms of symptoms or duration. In fact, the one person in the group who was the most up-to-date with both vaccinations and boosters was the one who had the most difficult time getting over the infection.
Does that mean vaccinations and boosters are bad? Of course not. They are designed to protect against something that is known to exist, not against something that is unknown to exist. So when something that was previously unknown such as Omicron comes along, the prior vaccines can't be relied on for protection as all the people in my travel group would tell you.
Therefore, the best possible protection against Omicron is to have already had Omicron. Now eventually I'm sure an Omicron-specific vaccine will be available and that would be a smart choice for anyone that has never been infected with Omicron.