Add CI check for warnings & errors when building docs

[tlylt]

What is the purpose of this pull request?

• Documentation update
• Bug fix
• Feature addition or enhancement
• Code maintenance
• DevOps
• Improve developer experience
• Others, please explain:

Overview of changes:
Related to #2140

Add a step to check if there are any warnings/errors when building our documentation (UG + DG), which is deployed at markbind-master. This helps to ensure that we are not accidentally pushing any broken links and any sort of other issues reflected in our documentation unexpectedly.

So far our documentation does not contain any warning (and error) unless there's a problem. Hence, this CI check is made to fail when it detects a warning, effectively forcing the developer to investigate and eliminate the warning.

Anything you'd like to highlight/discuss:
nil

Testing instructions:
See the following screenshot when there is a warning (for details, check the past CI runs https://github.com/MarkBind/markbind/actions/runs/4711997883/jobs/8356766412).

• When there's no warning, the check will pass
• When there's a warning:
  
  
• The developer can then check the step before to see the details
  

Proposed commit message: (wrap lines at 72 characters)
Add CI check for warnings & errors when building docs

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Checklist: ☑️

• Updated the documentation for feature additions and enhancements
• Added tests for bug fixes or features
• Linked all related issues
• No unrelated changes

[jovyntls]

LGTM! Thanks @tlylt, this is a useful feature & good idea that would have caught lots of our previous bugs :)