  We independently determine the zero-point offset of the Gaia early Data
Release-3 (EDR3) parallaxes based on $\sim 110,000$ W Ursae Majoris (EW)-type
eclipsing binary systems. EWs cover almost the entire sky and are characterized
by a relatively complete coverage in magnitude and color. They are an excellent
proxy for Galactic main-sequence stars. We derive a $W1$-band Period-Luminosity
relation with a distance accuracy of $7.4\%$, which we use to anchor the Gaia
parallax zero-point. The final, global parallax offsets are $-28.6\pm0.6$
$\mu$as and $-25.4\pm4.0$ $\mu$as (before correction) and $4.2\pm0.5$ $\mu$as
and $4.6\pm3.7$ $\mu$as (after correction) for the five- and six-parameter
solutions, respectively. The total systematic uncertainty is $1.8$ $\mu$as. The
spatial distribution of the parallax offsets shows that the bias in the
corrected Gaia EDR3 parallaxes is less than 10 $\mu$as across $40\%$ of the
sky. Only $15\%$ of the sky is characterized by a parallax offset greater than
30 $\mu$as. Thus, we have provided independent evidence that the parallax
zero-point correction provided by the Gaia team significantly reduces the
prevailing bias. Combined with literature data, we find that the overall Gaia
EDR3 parallax offsets for Galactic stars are $[-20, -30]$ $\mu$as and 4-10
$\mu$as, respectively, before and after correction. For specific regions, an
additional deviation of about 10 $\mu$as is found.
