This is only true if you consider anything less than 100% protection to be a failure. What the study actually says is that the protection provided by the vaccine decreases somewhat - not completely - over time:
"while functional neutralization by vaccine-primed sera is considerably blunted against B.1.1.529 (Omicron), three-dose vaccination efficacy against symptomatic disease holds up, in the 50-70% range"
This is only true if you consider anything less than 100% protection to be a failure. What the study actually says is that the protection provided by the vaccine decreases somewhat - not completely - over time: "while functional neutralization by vaccine-primed sera is considerably blunted against B.1.1.529 (Omicron), three-dose vaccination efficacy against symptomatic disease holds up, in the 50-70% range"
Follow the link and read it yourself. (https://onlinelibrary.wiley.com/doi/10.1111/andr.13209)
OP is misrepresenting the research when they claim "booster shots don't work".