This is just an anecdote, but maybe informative to share. I'm just one individual, but it might provide some perspective in what a fully vaccinated person might expect if they are exposed to COVID.
For background, I'm a family physician and completed my vaccine series in January. When the pandemic hit, the hospital I work for instituted a special "respiratory care clinic" where we can address patients with respiratory ailments in a separate location, under full PPE, in a negative pressure exam room, and isolated from patients. I work in this clinic about twice a month.
I won't go into the level of irresponsibility showed by this particular patient, but briefly, this week I saw a young woman for a very minor skin issue who we knew had tested positive for COVID. Even with her wearing a mask, and myself and the nurse in full PPE, I could literally see the clouds of respiratory secretions as she coughed heavily throughout the exam (I denied her request to remove the mask, because it made her "uncomfortable").
About a day later, I started to experience some of those vague feelings you get before an illness. Nothing severe, I just felt off. Then, I became mildly congested. Fearing for what may have been on the way, I isolated myself at home away from my wife (waiting for her second dose), 2 year old son (obviously not vaccinated yet), and two dogs, one of whom was very upset with this situation.
Luckily, the symptoms never progressed beyond extremely mild, and they're now gone. Despite being fully vaccinated and wearing full PPE, I have no doubt that what I experienced was my immune system fighting off COVID. Unknowable at this time is if I was actively shedding viral particles until my immune system finished the job.
So, my take home was that the vaccine worked. But rather than making me completely invulnerable to COVID, a better description would be that the vaccine stacked the deck in my favor, and made it an unfair fight for the virus. But it didn't prevent the fight from occurring altogether.