A few kpc is much more than 1% the size of the Milky Way. For reference, the Sun is about 8 kpc from the Galactic Center.
For bright stars, Gaia can measure parallaxes (and therefore distances) throughout a sizeable fraction of the Milky Way. But the fainter the star is, the closer it has to be for Gaia to measure its parallax. The other issue is that there's dust that obscures much of the Galaxy, limiting the range that Gaia can see to. If you take all these effects into account, you find that Gaia can "only" measure parallaxes for about 1% of the stars in the Milky Way. Still, that's orders of magnitude more stars than had parallaxes just a few years ago.
For bright stars, Gaia can measure parallaxes (and therefore distances) throughout a sizeable fraction of the Milky Way. But the fainter the star is, the closer it has to be for Gaia to measure its parallax. The other issue is that there's dust that obscures much of the Galaxy, limiting the range that Gaia can see to. If you take all these effects into account, you find that Gaia can "only" measure parallaxes for about 1% of the stars in the Milky Way. Still, that's orders of magnitude more stars than had parallaxes just a few years ago.