I'm pretty sure that it's referring to your client sessions, so every time you start your game, regardless of how much you'll keep it open, this number will be incremented by one. I also can tell that the fact that EAC is bypassed doesn't influence the counter, even though I haven't tried with an offline bypass method (I believe that currently, the only way to accomplish this, even though it's kinda useless, is by turning off the firewall rule from the old bypass method).
Probably in any context where the json mentions "session", it refers to what I explained.
I can't tell how much safe it is to change the cumulative sessions manually and inject it by the way, because God knows whether something online (such as Steam) records that value as well, and if they compare the one in your save file with the online one it'll probably result in a ban since they're supposed to be synced; actually anything in the json save file that is synced with online stuff, like the Shrine of Secrets, does never get affected by any kind of modification through save file editing since it'll refresh every time you start the game, but still who knows.
