Shipping products implies real things and physics that work. What they say on the aptera website seems entirely reasonable: 700 watts of solar power good for up to 40 miles per day.
Basically this vehicle is very efficient so doing 40 miles while soaking up 6-10 hours x 700 = about 4-5 KWH seems doable. A Tesla would do about 4-5 miles/kwh. This thing is lighter, more slippy, and has one wheel less so it's probably a bit better than that. This car is covered in small panels and has a surface area that is probably 6-8 square meters. let's call it 7. 100w/square meter is not unreasonable. Probably it's a bit higher than that and the effective square meters of solar is a bit lower. But 700watt is not a strange number for a car that size.
The 25K model obviously does not have a 100KWH battery; that would be the top model which is presumably a lot heavier and logically less efficient and twice the price according to the article. Nobody is claiming that that vehicle would do 1000 miles on just solar power.
If you think about it, with such a huge battery, you could do 20 50 mile journeys without plugging in even without solar. Or about a month of commutes. And it would add 20-40 miles back in every day. And since this company is based in California, they get a lot of sunlight there so I could see how that would average closer to 40 than to 20.
Assuming you are not commuting on weekends it would either take months to drain the battery or you'd manage to keep it topped up with just the sun. And when you do run out eventually, you just plug it in and deal with it. If that happens a couple of times per year, so what? And you can go on a long journey and just fast charge and then most of the time when you don't do that, you just rely on the sun topping you up. Seems, like a great value proposition for people with a bog standard 10-20 mile commute. 365*40=14600 miles per year. Most drivers don't do that in a year. Probably the 25K model is all they'd ever need.