It’d take more than twice as much fuel
The escape velocity of the sun when you start at Earth is a bit under 60 km/s, but you start at 42 km/s which is Earth’s orbital velocity so to leave you need to just add another 18 km/s in the same direction as the current orbit and you’re good
If instead you burn north/south(perpendicular to the plane the planets orbit in) then Pythagoras says you’d need to add about 42 km/s of speed in that direction to get the 60 required to leave, that’s over twice the speed and way over twice the fuel required
From a fuel perspective it’s better to burn outwards, fly past Pluto, stop, then fly north in the same way it takes less fuel (but more time) to fly out and stop and fall back towards the sun than to slow down to get to the sun
For the most part though we’re only launching probes to look at things in our system so we stick with launching them out towards the outer planets because getting to anything interesting beyond our system would likely take a century or more even if that’s the only goal
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