Please add the euiResizable directive on the panel to get the same feature.
<eui-layout #layout style="width:700px;height:250px;">
<eui-layout-panel euiResizable handles="e" region="west" style="width:120px;"
(resizing)="layout.updatePaddings()">
<p>West Region</p>
</eui-layout-panel>
<eui-layout-panel region="center" style="height:100%">
<p>Center Region</p>
</eui-layout-panel>
</eui-layout>