Yes, weight is definitely worth considering if this is primarily something you’ll carry while traveling and hiking. One important point about the Anker Zolo 20K 30W, though: because it is still a 20,000 mAh battery, it isn’t dramatically lighter simply because it has fewer connections. The Zolo 20K 30W with the built-in USB-C cable weighs about 318 grams (11.2 oz). It also actually provides a built-in USB-C cable, a USB-C port, and a USB-A port, so you can charge more than one device, although you won’t get the full 30W output when charging multiple devices simultaneously.
If your main concern is reducing what you have to carry on the trail, I would consider whether you really need 20,000 mAh. The 30W rating tells you how quickly the power bank can deliver power; the 20,000 mAh rating is what largely determines how much stored energy—and therefore battery weight—you’re carrying. Moving to a 10,000 mAh power bank could make a much more noticeable difference in weight while still providing roughly two additional phone charges, depending upon the phone and actual charging conditions.
Regarding the Nano appearing completely dead when you received it: I wouldn’t consider that alone evidence that it will be unreliable. Lithium-ion power banks can arrive with a very low state of charge, particularly if they have been sitting in inventory for some time. I would connect it to a good USB-C PD charger, allow it to charge for several hours, and then test it. If it charges normally, retains its charge, and can subsequently charge your phone normally, I wouldn’t be particularly concerned. On the other hand, if it repeatedly refuses to charge, loses a substantial amount of charge while sitting unused, becomes unusually hot, or behaves erratically, I would exchange it rather than trust it while traveling.
And you are correct about airline baggage. Power banks are considered spare lithium-ion batteries and, under current FAA rules, they cannot be placed in checked baggage. They must travel with you in your carry-on baggage. A typical 20,000 mAh power bank is below the FAA's 100 Wh limit for ordinary passenger carry-on use, although an individual airline can impose additional restrictions.
Given how you plan to use it, I would put more emphasis on finding the capacity you actually need than simply choosing between two different 20K models. If you rarely need several full phone recharges between opportunities to plug in, I think a good 10K USB-C PD power bank may be a much better travel companion. You would give up some reserve capacity, but you'd actually notice the reduction in your bag or backpack.