Example of how to open GridContextMenu with the left click on the icon while opening it with the right click elsewhere.

GridContextMenuView.java

package com.example.application.views;

import java.util.Optional;
import java.util.Random;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

import com.vaadin.flow.component.Component;
import com.vaadin.flow.component.Focusable;
import com.vaadin.flow.component.Key;
import com.vaadin.flow.component.Shortcuts;
import com.vaadin.flow.component.grid.Grid;
import com.vaadin.flow.component.grid.Grid.Column;
import com.vaadin.flow.component.grid.Grid.SelectionMode;
import com.vaadin.flow.component.grid.contextmenu.GridContextMenu;
import com.vaadin.flow.component.html.Div;
import com.vaadin.flow.component.icon.Icon;
import com.vaadin.flow.component.icon.VaadinIcon;
import com.vaadin.flow.component.textfield.TextField;
import com.vaadin.flow.component.textfield.TextFieldVariant;
import com.vaadin.flow.data.binder.Binder;
import com.vaadin.flow.router.Route;

@Route(value = "grid", layout = MainLayout.class)
public class GridContextMenuView extends Div {

    Grid<Pojo> grid = new Grid<>();

    private Optional<Pojo> item;
    private Optional<Column<Pojo>> column;

    private GridContextMenu<Pojo> menu;

    public GridContextMenuView() {
        TextField valueField = new TextField();
        valueField.setWidth("100%");
        TextField textField = new TextField();
        textField.setWidth("100%");
        valueField.addThemeVariants(TextFieldVariant.LUMO_SMALL);
        textField.addThemeVariants(TextFieldVariant.LUMO_SMALL);
        valueField.setAutoselect(true);
        textField.setAutoselect(true);
        grid.getStyle().set("--lumo-space-xs", "1px");
        grid.getStyle().set("--lumo-space-m", "1px");
        Binder<Pojo> binder = new Binder<>();
        binder.forField(valueField).bind(Pojo::getValue, Pojo::setValue);
        binder.forField(textField).bind(Pojo::getText, Pojo::setText);
        grid.addColumn(Pojo::getValue).setEditorComponent(valueField)
                .setHeader("Value").setSortable(true).setResizable(true);
        grid.addColumn(Pojo::getText).setEditorComponent(textField)
                .setHeader("Text").setSortable(true).setResizable(true);
        grid.getEditor().setBinder(binder);
        grid.getEditor().setBuffered(true);
        grid.setSelectionMode(SelectionMode.NONE);
        menu = grid.addContextMenu();
        grid.addContextMenu().addItem("Edit", e -> {
            if (grid.getEditor().isOpen()) {
                grid.getEditor().save();
            }
            e.getItem().ifPresent(pojo -> {
                grid.getEditor().editItem(pojo);
            });
        });
        grid.addCellFocusListener(e -> {
            item = e.getItem();
            column = e.getColumn();
            item.ifPresentOrElse(pojo -> {
            }, () -> grid.getEditor().save());
        });
        grid.addComponentColumn(item -> {
            Icon icon = VaadinIcon.MENU.create();
            icon.addClickListener(e -> icon.getElement()
                    .executeJs("const y = this.getBoundingClientRect().top;"
                            + "const x = this.getBoundingClientRect().left;"
                            + "const ev = new MouseEvent('contextmenu', {"
                            + "    'view': window,"
                            + "    'bubbles': true,"
                            + "    'button': 2,"
                            + "    'cancelable': true,"
                            + "    'x': x,"
                            + "    'y': y"
                            + "});"
                            + "this.dispatchEvent(ev);"));
            return icon;
        }).setFrozenToEnd(true);
        grid.setWidth("400px");
        grid.setItems(IntStream.range(1, 1000).mapToObj(i -> randomString())
                .map(s -> new Pojo(s)).collect(Collectors.toList()));
        Shortcuts.addShortcutListener(grid, e -> {
            item.ifPresent(item -> {
                if (grid.getEditor().isOpen()) {
                    grid.getEditor().save();
                } else {
                    grid.getEditor().editItem(item);
                    column.ifPresent(column -> {
                        Component component = column.getEditorComponent();
                        if (component instanceof Focusable) {
                            Focusable<?> field = (Focusable<?>) component;
                            field.focus();
                        }
                    });
                }
            });
        }, Key.ENTER).listenOn(grid);
        add(grid);
    }

    // Create String of 4 random characters from the set [a-z]
    private static String randomString() {
        Random random = new Random();
        return random.ints(4, 97, 123).mapToObj(i -> String.valueOf((char) i))
                .collect(Collectors.joining());
    }

    public class Pojo {
        private String value;
        private String text = randomString().toUpperCase();

        public Pojo(String value) {
            this.value = value;
        }

        public String getValue() {
            return value;
        }

        public void setValue(String value) {
            this.value = value;
        }

        public String getText() {
            return text;
        }

        public void setText(String text) {
            this.text = text;
        }
    }
}

I suppose we can use these ClickEvent properties: e.getScreenX and e.getScreenY, worked for me.

Yes. There are variations of the approach you can use.

There is feature request here: vaadin/flow-components#3606