Up until they did this ALL vaccines had to meet certain criteria:
1. The injection must give you antibody immunity to the virus.
2. Those antibodies must protect you from that virus.
3. The injection must show that it reduces hospitalizations- sickness, symptoms and deaths related to that virus.
4. The injection must protect and prevent the person who receives it from carrying that bacteria or virus.
5. The injection must prevent those who receive it from transmitting that virus.
Those are the things required of injections to be considered a vaccine- by definition.
No. For example, the polio vaccines do not necessarily prevent you from being infected with the polio virus; they protect you from severe illness caused by the virus. In fact, the most commonly-used polio vaccine actually gives you a dose of attenuated live polio virus, which proliferates in your body, producing immunity. Yellow Fever and smallpox vaccinations were like that, too. So are measles vaccines.
When people first started doing vaccinations, they really had no idea what was going on, so very little of that stuff in your definition was even known. They just knew that if one was exposed to a weak version of an infectious agent, or to parts of a killed suspension of microorganisms, immunity would often follow.
Of course, the COVID-19 vaccines do indeed give you very good immunity to the virus; your likelihood of being infected after vaccination is much less than if you are not vaccinated. And the likelihood of being very ill or dying is much , much less. Those data have been posted here repeatedly. Would you like to see them, again?
And of course, if you have much less chance of being infected, you have much less chance of spreading the infection. For reasons you can probably realize.
And the definition of a vaccine in science is:
A preparation of killed or live disease organisms, or fragments of organisms that are introduced into the body to produce immunity.
That hasn't changed since the 1960s, when I first learned that definition from my biology classes.
Your "definition" vaguely resembles Koch's Postulates, which is meant for something else. It was the way that Koch proposed to test microorganisms as agents of disease.