The other last-modified-plugin is now archived, and no longer included in the default Jekyll, but the sitemap and seo plugin still seem to rely on the page.last_modified_at property, albeit undocumented (https://github.com/jekyll/jekyll/issues/9702), so might be worth getting the implementation switched upstream perhaps?
We show the last-modified date on endoflife.date products (https://endoflife.date/jekyll), but I'm not sure how we have the property set right now, since I don't remember including either plugin. Thanks for creating this, I have a few other sites where this will be quite helpful.