Yeah, TLV on a Friday evening (or Saturday until Shabbat ends, which is right about now if my time zone and web sundown calculation is correct) is not the most exciting place to hang out. Other nights all of the shops and restaurants in that long area behind the checkin counters (before security) are a reasonable way to kill a couple hours, but at least when I was there on a Friday night a few months ago, the only thing open was one of the coffee stands.

You'd still have to carry your luggage around, but at least something to do. You're not missing anything, that's kind of just the way it is at TLV. All of the airlines with just a flight or two don't open checkin until 3 hours before; I've heard sometimes you can check in earlier for El Al...but they don't fly or open the counters on Shabbat at all (they do after it ends for their Saturday night flights), so that's moot.

At least once you get checked in, most of the post-security shops (plus your lounge) should be open -- about half to 3/4 were even on the Friday night I was there. Maybe the food will even be fresh after sundown (Burger Ranch was the only thing open, and I'm pretty sure they were only serving reheated food during Shabbat because they're Kosher).

Sorry it didn't work out the way you planned.