Sort posts by updated and published date

I am trying to understand your question here. Jekyll will always sort your list of posts descending, by the date field, so the latest post shows first.

Each post has front matter, like this:

---
title: My post
date: 12-01-01
layout: post
---
This is my blog post...

The following code will always sort the list of posts descending using that date field, so the last post is the latest:

{% for post in site.posts %}
  <p><a href="{{ post.url }}">{{ post.title }}</a>
{% endfor %}

If you want to sort by some other field, then absolutely, you can use the front matter as you propose. Here is what that might look like using your example:

---
title: My post
date: 12-01-21
last_updated: 12-08-21
layout: post
---
This is my blog post...

And you would sort this way:

{% assign posts = site.posts | sort: 'last_updated' | reverse %}
{% for post in posts %}
  <p><a href="{{ post.url }}">{{ post.title }}</a>
{% endfor %}

Of course if you can remove the reverse option to sort ascending.

Hope that helps!