A search for neutrinoless double-beta decay ($0 ubetabeta$) in $^{136}$Xe is performed with the full EXO-200 dataset using a deep neural network to discriminate between $0 ubetabeta$ and background events. Relative to previous analyses, the signal detection efficiency has been raised from 80.8% to 96.4$pm$3.0% and the energy resolution of the detector at the Q-value of $^{136}$Xe $0 ubetabeta$ has been improved from $sigma/E=1.23%$ to $1.15pm0.02%$ with the upgraded detector. Accounting for the new data, the median 90% confidence level $0 ubetabeta$ half-life sensitivity for this analysis is $5.0 cdot 10^{25}$ yr with a total $^{136}$Xe exposure of 234.1 kg$cdot$yr. No statistically significant evidence for $0 ubetabeta$ is observed, leading to a lower limit on the $0 ubetabeta$ half-life of $3.5cdot10^{25}$ yr at the 90% confidence level.
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