First, the case documents are available on the Court's site ((1) Petition + lower courts' decisions, annexed; (2) Brief of respondent J. W., a Minor in opposition; (3) Reply of petitioner Watchtower NY).
blondie, careful,
The case you're referring to (the Padron case) was settled twenty months ago.
In this case a judge punished the Watchtower for refusal to produce certain documents (files received by it in response to the 1997 BOE letter) by entering default judgment against them and awarding a plaintiff $4 million without trial. An appellate court affirmed that ruling thus creating a pretty dangerous (for the org) precedent.
smiddy3,
Mere filing of a petition doesn't stay or suspend execution of appealed decisions. This petition didn't "delay a judgment". And since the Watchtower posted a $6,024,228.58 appeal bond on August 15, 2016, the compensation has likely been paid months ago, probably shortly after the appellate court issued its judgment on December 10, 2018
I don't know the exact reason why this petition was filed. Maybe they really tried to overturn the precedent established by a Californian court, or maybe it's just their modus operandi to appeal negative rulings as far as possible - to the best of my knowledge, this case is the first and the only CSA case lost by WT which hasn't eventually been settled.