Go with Bialetti, you buy it once and you shouldn't ever need to replace it. $35 and you have it for life.
https://www.amazon.com/Original-Bialetti-Moka-Express-Stovetop/dp/B0000CF3Q6/ref=sr\_1\_3?keywords=bialetti+moka+pot&qid=1685335499&s=home-garden&sprefix=Bialetti+%2Cgarden%2C368&sr=1-3

All the deep-somethings are based on the lead-acid reaction. Sometimes a bit more chemistry gets added. It will buy you a few more cycles, maybe a bit more discharge head room. But ultimately the quoted Ah is for a non-rechargable setting. You can pull the full Wh/Ah out of the battery, it's totally doable. Exactly once.

Car level lead acid batteries actually start to die if you go beyond 30% discharge. 50% is already the optimistic opinion in a daily cycle usecase. As you don't cycle often, a 60-65% discharge cutoff might work.

You could go hipster and use a solar power station. More expensive, less DIY work and it can go used elsewhere without issues. They are light enough to take them home. Fast charge with the generator, maybe scale down the gaming a notch or 3. A smaller battery isn't a killer if you can recharge while the coffee is brewing. And you could even use the cheaper, lighter NCM LiIon stations. You don't need the cycle count of a lifepo4 battery. Jackery is one big brand for those.

About coffee and campfire: https://www.amazon.com/Original-Bialetti-Moka-Express-Stovetop/dp/B0000CF3Q6 and something heat resistant to keep the temperature reasonable. No artificial noise at all and it will keep up talking the whole night.