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Sounds like a cheaper version of the NeoAir XLite I was looking into a while back:
https://www.amazon.co.uk/Thermarest-Therm-a-Rest-NeoAir-Xlite-Mattress/dp/B00BP64P1I230g for the Small. 23 x 9 (cm) pack size.
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I've got the slightly heavier duty version of that one. You can get a small light pump for it that runs off a single AA battery which is pretty handy. Leave it for a couple of minutes while you're sorting other stuff out and it's pretty much ready to go. Combined they pack down smaller and lighter than a foam roll.
On a very different level of extremity, I've been touring with one of these and they're so comfortable, light and pack down so small I can't see why I'd choose anything else. It takes 2 mins to inflate, which surely isn't that much of a penalty? Never feel the floor through them (even when basically lying on logs/bricks) and get a great night's sleep. Yoga mats/self-inflating mats never give me that level of comfort, which I value over the two mins of inflation... I guess potential problem is they could puncture, but if you have a repair kit there's no massive risk and they seem pretty sturdy...