I bought a couple of Schumacher Mini-Mite (12 Ah) jump starters in 2006. One reason I liked it was that it had the AC plug built in although it was recessed. It charged at about 1-2A (not sure) and often I'd just use a 3 prong adapter and a cheap extension cord, although I think the general idea was to use a heavy duty extension cord like you'd use with electric outdoor equipment.
That used a sealed lead acid battery. I suppose it might be possible to replace it, but I remember paying $40 each for them with free shipping from Amazon. Also back when they didn't directly charge sales tax for sales to California, although I theoretically needed to pay a California use tax.
I gave one to my parents but I highly doubt they bothered to charge it although I might have charged a few times when I was there. It wasn't working after about 10 years. I'm not even sure it was ever used to jump start a car. Mine was inconsistently charged over the years, but I believe the recommendation was to fully charge it at least every 3 months and any time after use.
I was still working until about 2018. I'm not sure how many jump starts it's gone through, but it's got to be at least a dozen times. My wife had a habit of leaving the map lights on and there was a problem with the door sensor where the headlight warning didn't work. I recall at least a couple of times where I offered it to a stranger in a parking lot, and at least three times when a coworker mentioned that a car wouldn't start. Once a coworker borrowed it for her husband to use, but then came back to me telling me that it just died again since he didn't drive it more than a couple of miles. I lent my 1.5 A charger and said he should charge it overnight even it wasn't full.
I used it once to just charge my phone when I went camping and didn't want to drain my car battery.
It started getting weak around 2018. So it lived a good life.