If Voyager 1 hasn't passed through the Oort Cloud, how can it be said to have left the Solar System?
The Solar System is not conventionally defined as the full range of the Sun's gravity. It's the more limited range of a stream of particles coming from the Sun -- the solar wind.
The solar wind is a stream of particles blowing out from the Sun in all directions. To quote the reference given below, it's like the cloudy breath you see in front of you when you exhale on a cold day. If the air around you were perfectly still your breath would go on forever. But with the actual moving air of our atmosphere your breath gets incoroporated into those air currents. Similarly the solar wind ultimately gets incorporated into currents of rarefied gas in interstellar space, the interstellar medium.
The edge of the Solar system is defined as the boundary, or heliopause, where the solar wind gets incorporated into the interstellar medium.
As you point out, the Sun's gravity predominates far beyond the heliopause, through the Oort Cloud that goes maybe a couple light years from the Sun. We then say that the Sun's gravity pulls in things not only from within the Solar System, but also from neighboring parts of interstellar space.
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