An example of how a UI Toolkit TextField Suggestion field could be created

gistfile1.txt

using UnityEditor;
using UnityEngine;
using UnityEngine.UIElements;

public class TextEditorWindow : EditorWindow
{
    VisualElement m_Suggestion;
    TextField m_TextField;

    [MenuItem("Test/Window")]
    static void ShowWn()
    {
        CreateWindow<TextEditorWindow>();
    }
    
    private void OnEnable()
    {
        m_TextField = new TextField();
        m_TextField.RegisterValueChangedCallback(TextChange);
        rootVisualElement.Add(m_TextField);
        rootVisualElement.Add(new Label("Some Label"));
        rootVisualElement.Add(new Button { text = "Some Button" });
    }

    void TextChange(ChangeEvent<string> evt)
    {
        if (m_Suggestion == null)
        {
            m_Suggestion = new VisualElement
            {
                style =
                {
                    backgroundColor = new Color(0.3f, 0.3f, 0.3f),
                    borderTopColor = Color.black,
                    borderBottomColor = Color.black,
                    borderLeftColor = Color.black,
                    borderRightColor = Color.black,
                    borderLeftWidth = 1,
                    borderBottomWidth = 1,
                    borderRightWidth = 1,
                    borderTopWidth = 1,
                    position = Position.Absolute,
                }
            };
            rootVisualElement.Add(m_Suggestion);
        }

        m_Suggestion.Clear();
        for (int i = 0; i < Random.Range(5, 10); ++i)
        {
            var text = System.Guid.NewGuid().ToString();
            var label = new Label(text);
            label.RegisterCallback<MouseDownEvent>(evt =>
            {
                m_TextField.SetValueWithoutNotify(text);
                m_Suggestion.RemoveFromHierarchy();
                m_Suggestion = null;
            });

            m_Suggestion.Add(label);
        }

        m_Suggestion.style.top = m_TextField.layout.yMax;
    }
}

You could do more like change focus when you press up/down with the mouse and press return etc
This version needs you to click on the text