How will vaccine requirements for public/private amenities/services work when we're at, say, the 4th or 5th booster? Will people who just got their initial shots but haven't gotten any boosters, or even the most current booster, essentially be "unvaccinated" at that point in regards to being granted entry/access to those places and services?
That would depend on how well they work. The future is still uncertain and lots of things can change. Maybe the next iteration of the vaccines will be super effective against Delta, and that combined with a widespread global rollout will eliminate it from our population. On the other end of the spectrum, maybe a new variant emerges that is even more infectious than Delta, and also different enough that our vaccines prove ineffective against it.
We don't know, which is why continued testing and study is important. Right now, we have already completed lots of research that says our current vaccines are about 40%-80% effective at preventing delta infection, and 90%+ effective at preventing hospitalization and death. Preliminary research out of Israel is suggesting that the boosters are having a positive effect.
Once new vaccines are developed or new variants emerge, there will need to be additional tests done to see how long the vaccine protection lasts and if boosters are necessary, and if so at what interval. There's so many things we don't know yet, which is why it's important to figure it out.
Once a clearer picture emerges due to data, then the recommendations can be set. Until then, we're doing the best we can with the data and tools available to us now.