Yup, it's possible to get a disease you're vaccinated for, just a lot less likely. This is true for every vaccine ever invented - you were just unlucky, as these (especially mRNA ones) are extremely good at preventing even infection.
"Booster" is somewhat of a misnomer. A lot of vaccines require multi-dose regimens to confer lasting immunity (remember getting the Hepatitis vaccine? There were 3 doses that are spaced 6 months apart I believe). A minimum 6 month spacing is considered optimal for desired immune response, and it was always suspected that this would be the case. The initial doses were spaced 3 or 4 weeks apart as a compromise to quickly verify efficacy while still providing a decent amount of lasting protection, and to quickly give a large amount of people "good enough" protection.
As someone who had covid
@CoElkHunter and had the vaccine, you should be pretty well protected from becoming infected again for a while, but of course this is highly dependent on a variety of factors, including your individual immune response. Scientists are in the process of measuring antibody levels and trying to answer a lot of these questions.
This will end (pandemic), despite the new variants popping up. The Moderna vaccine has proven to be remarkably effective at even preventing infections of the Delta variant, even 6+ months post vaccination (the longest time period we have good data for). The virus will never be eliminated in humans, but will simmer in the background, out of mind like countless other contagious human pathogens.
