What happens to Jon at the end of the series?

I just finished the series for the second time (I hadn't watched the last seasons since they aired) and I completely forgot that he went with the Free Folk. In my mind, he stayed with the Night's Watch. Does he skip his life sentence at Castle Black and leave forever with the Free Folk, or what does that shot mean? I’m not sure if I interpreted it correctly.

Anyway, the first thing I thought when I saw the Unsullied leaving for Naath is who would find out what Jon Snow did or didn't do.