To-Do Block: check/uncheck tasks from Reader doesn't work

iOS issue: https://github.com/wordpress-mobile/WordPress-iOS/issues/16792

Expected behavior

When I tap on a task, the task is marked as done (strikethrough) and my @ is added after it between parenthesis. Just like it is on the web.

Actual behavior

Tapping on the task does nothing.

Steps to reproduce the behavior

1. Create a post in an internal P2 and add a To-Do list block
2. Add a few tasks
3. Open this post on Reader
4. Tap on any of the tasks
5. Nothing happens

Technical details

In order for this to work on mobile Reader, we would need:

1. When a task is tapped, the native application needs to trigger a request
2. We need to manipulate the HTML to mark the task as "done"

The big issue I see here is the request. By doing a quick investigation (you can just use your browser to do the same) it seems to me that what happens when a task is marked as done is that a request to update the content of this post is triggered. This is tricky to do from the Reader because sometimes what we have is just the HTML output (even with some stuff cleaned). If we use that to update the post, we might end up breaking it (and removing the block declarations).

Ps.: it worths noting that this issue doesn't affect end users, given to-do block is used on internal P2s.

Start by reproducing the Reader behavior described in the issue with a post containing a To-Do list block, then compare it with the linked iOS issue and the web behavior. Trace how Reader obtains and updates post HTML, especially the request needed when a task is tapped. Done means tasks can be marked complete in Reader without removing block declarations or otherwise breaking the post.