The escape velocity is what you’d have to have as you’re on the surface – so, like, if you threw a rock it would have to come off your fingers at 11200m/s to escape.
As you say, if you had a rocket with an insane amount of fuel, you could rise as slow as you wanted (one centimeter per day, or whatever) and eventually escape. But the escape velocity is for if you don’t get a rocket, just one burst at the start, as if you were shot out of a cannon.
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