I don't think they are usually labeled the way you describe, as there would be no way of knowing, just from the labeling, if F1 seeds were the original cross, or if they were seeds from an F1 plant.
Heres the way I see it. The seeds that came from
the F6 plants are F6 seeds. Planted this season they
will produce the F7 plants/pods/seeds. Thus, the F7
So, the seeds marked F2 mentioned above will produce
F3 plants/pods/ seeds the following season.
I think that makes sense to me, but I could be
all wet 😜