This is correct. Planetary gravitational slingshots work with respect to Sun-relative velocities. Trying to use the Sun to slingshot out of the solar system i

This is correct. Planetary gravitational slingshots work with respect to Sun-relative velocities. Trying to use the Sun to slingshot out of the solar system is like trying to use Earth's gravity to sling into Earth orbit. Being at the bottom of a gravity well cannot help you to leave it. It's like riding a bike down a hill; you can't then use the kinetic energy to roll up a bigger hill than you started from. A gravity assist works by robbing orbital momentum from the planet, transferring it to the spacecraft. (I once saw a calculation that Voyager's slingshot slowed Jupiter's motion by one foot per trillion years.) Jupiter has orbital momentum around the Sun, but the Sun has no orbital momentum around itself. Flying past the Sun could give you velocity relative to the galactic center, making use of the Sun's orbit around that. But that velocity doesn't help you leave the Sun's neighborhood or travel within the Solar System, because the gained velocity is in the same direction as the Sun and Solar System are already moving.