= Solution
The <universal kriging> model has a linear drift in $y$ and a zero-mean Gaussian residual field:
$$
Z(x,y)=\beta_0+\beta_1y+W(x,y),\qquad \operatorname{Cov}(W(s),W(t))=\sigma^2e^{-(\|s-t\|/a)^2}+\tau^2\mathbf1_{\{s=t\}}.
$$
The `Gau` range parameter in this software is $a=1/\phi$, since its <semivariogram> uses $1-e^{-(h/a)^2}$. The output gives $\widehat\tau^2=0$, $\widehat\sigma^2=0.4726257$, and $\widehat a=1.112235$, hence $\widehat\phi\simeq0.899091$. The exact Gaussian range is infinite; the 95-percent <practical range> is approximately $1.92508$ in the coordinate distance units.
The https://r-spatial.github.io/gstat/reference/predict.gstat.html[`BLUE=TRUE` option] asks for the <best linear unbiased estimator> of the drift, rather than the full field <kriging> prediction. Thus the two printed fitted trends give $\widehat\beta_0=20.13793$ at $y=0$ and $\widehat\beta_0+\widehat\beta_1=22.08399$ at $y=1$. Therefore
$$
\boxed{\widehat m(x,y)=20.13793+1.94606y,\quad\widehat\tau^2=0,\quad\widehat\sigma^2=0.4726257,\quad\widehat a=1.112235.}
$$
There is no $x$ coefficient in the drift. The reported <variances> $0.09456496$ and $0.06097459$ are the <variances> of the corresponding estimated trend values, not full-field prediction <variances>. They do not determine the slope <variance> without its <covariance> with the intercept. The interpolated map can still vary with $x$ through the correlated residual prediction, even though the fitted deterministic drift depends only on $y$.
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