I know that I can register my model as a Django model and add an image there but I need to save a pages' tree and identify my pages by an image on a listing page. To make a long story short, I need to show images on the listing page in admin.
If you just want to add image, you don't need to override entire page title explore template. You can use just pages_listing_title_extra
block.
Create file templates/wagtailadmin/pages/listing/_page_title_explore.html
with content:
{% extends "wagtailadmin/pages/listing/_page_title_explore.html" %}
{% load wagtailimages_tags %}
{% block pages_listing_title_extra %}
{% image page.image fill-100x200 %}
{% endblock pages_listing_title_extra %}
This should not break with new version of Wagtail (only if this template block would be removed/renamed).