<xf:set var="$styles" value="{{ $xf.app.em.getRepository('XF:Style').getSelectableStyles() }}" />
<xf:set var="$targetStyleId" value="{{ $xf.options.defaultStyleId }}" /><!-- or some other style ID -->
Current style logo URL: {{ property('publicLogoUrl') }}<br>
Target style logo URL: {$styles.{$targetStyleId}.properties.publicLogoUrl}<br>