Am I correct in just taking 8 hours times 3000 mAh = 24,000 mAh
capacity would work? Or 8 hours times 36 Wh = 288 Wh capacity would
This is correct, these two statements are equivalent: 24 A-hr at 12 V is equal to 288 W-hr, just as 36 W consumed over 8 hours is equal to the same 288 W-hr.
Therefore, the solution to your power problem is a 12-V 24 A-h battery, which is about the size of the usual car battery. And therefore consider the corresponding weight of the power bank device. Designing a rechargeable and neat device out of raw battery has some engineering challenges, so in your case it is advisable to look for a consumer-grade solution.
There is an industry that serves this sector, it is "outdoor and recreation", they have portable power banks in the range of capacity you need, ~300 Whr and much more. Unfortunately these kind of devices also include DC-AC invertors to 120 or 220 V AC, which you don't need, and this adds to cost. Typical capacity of 12-V-only devices is marginally lower than you need for your wife's lamp. The best I could find is a 185 Wh power bank,
power bank 185 Whr
Maybe you will have a better luck in searching deeper. Unfortunately, manufacturers usually are not completely honest in their marketing efforts, and if some device with 5-12-20V output is "rated" as "50000 mAh", it likely means the mAh capacity either at 5V output, or at 3.7V Li-ion level.