Vaadin Tooltip API does not have method to set the CSS class name of a specific tooltip-overlay-element, which could be needed for specific styling cases. This JavaScript call is a workaround.

TooltipUtils.java

package com.example.application.views;

import com.vaadin.flow.component.Component;

public class TooltipUtils {

    public static void setTooltipClassName(Component comp, String className) {
        comp.getElement().executeJs(
        """
            if ($0.getElementsByTagName('vaadin-tooltip').length == 1) {
                $0.getElementsByTagName('vaadin-tooltip')[0]._overlayElement.setAttribute('class',$1);
            } else {
                const tooltips = document.getElementsByTagName('vaadin-tooltip');
                for (let i=0; i<tooltips.length; i++ ) {
                    const tooltip = tooltips[i];
                    if (tooltip._overlayElement.id === $0.getAttribute('aria-describedBy')) {
                        tooltip._overlayElement.setAttribute('class',$1)
                    }
                }
            }
         """, comp.getElement(), className);
    }
}