Those definitions aren't wrong, they're just not the only way a literal use of pull up has become a metaphorical one. "Pulling up your account" refers to the idea of lifting a sheet of paper or a file of papers from a drawer in order to look at it.
Some of the other meanings are complicated. Cars and buses can pull up to a curb (or kerb), boats can pull up to a dock, and a patron can "belly up" to the bar - these senses all have to do with reaching a destination, and with coming very close but not quite touching. Trains occasionally pull up to platforms, too. Not all stopping is pulling up. You can pull up at a red light, or your final destination, but other stops in the journey would not be described as pulling up.
Pulling you up to stop you, especially in the set phrase "pull you up short" refers to pulling hard on the reins of a horse - whether riding or driving - when you are above them. Pulling back means slow down and can be gentle. Hard yanking back and up stops the horse more quickly, and less pleasantly for all involved.
Finally the airplane one is pretty darn literal, referring to a control system where you pull towards you to make the plane go up, and push away from you to make it go down.