Are the covid vaccines gives protection ?

 The big picture of covid vaccination efficacy from CDC official site:

There is No waning in protection from death, among those who took 2 doses vs. 3 doses. Unvaccinated have 68x risk of dying of COVID-19.

Vaccinated people who get COVID-19 are less likely to report symptoms of long COVID, such as fatigue and shortness of breath, than are unvaccinated people, according to a new study. The research included more than 3,000 people in Israel and is one of the few studies so far to examine the effects of vaccination on long COVID. The results, which have not yet been peer reviewed, concur with a UK-based study from September, which found that vaccination halved the risk of long COVID.

CDC Recommends

• Everyone ages 5 years and older should get a COVID-19 vaccine as soon as they can.
• To get the most protection, get all recommended doses of a COVID-19 vaccine. Take all precautions until you are fully vaccinated.
• Everyone ages 16 years and older can get a booster shot either 6 months after their initial Pfizer or Moderna series, or 2 months after their initial Johnson & Johnson’s Janssen vaccine.

COVID-19 Vaccines Protect Against COVID-19 Infections and Hospitalizations