Add CI check for documentation deploy errors

[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:
Fixes #2335

Anything you'd like to highlight/discuss:
Did no include a check for deployment warnings because it will also capture false positives (when building UG and DG separately there are unavoidable warnings for broken links)

Testing instructions:
I tested the bash script locally, by

• cd docs
• markbind serve -d to serve the documentation site and also let it generate a log file in docs/_markbind/logs
• at this point the logs will have no "error" or warnings
• put the bash script in a file, e.g. test.sh

#!/usr/bin/env bash
log_file="docs/_markbind/logs/markbind-$(date +'%Y-%m-%d').log"
pattern="^[0-9T:.Z-]+ - error:"

if grep -q -E "$pattern" "$log_file"; then
printf "The following issues were found when deploying the documentation:\n"
grep -E "$pattern" "$log_file"
exit 1
fi

• then run bash test.sh, should observe nothing in the command line
• now change one of the log lines inside the log file from .... - info to .... - error
• rerun bash test.sh, should observe something like:

$ bash test.sh
The following issues were found when deploying the documentation:
2023-11-21T12:48:33.072Z - error: Pages built

Proposed commit message: (wrap lines at 72 characters)
Add CI check for documentation deploy errors

---

Checklist: ☑️

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

---

Reviewer checklist:

Indicate the SEMVER impact of the PR:

• Major (when you make incompatible API changes)
• Minor (when you add functionality in a backward compatible manner)
• Patch (when you make backward compatible bug fixes)

At the end of the review, please label the PR with the appropriate label: r.Major, r.Minor, r.Patch.

Breaking change release note preparation (if applicable):

• To be included in the release note for any feature that is made obsolete/breaking

Give a brief explanation note about:

• what was the old feature that was made obsolete
• any replacement feature (if any), and
• how the author should modify his website to migrate from the old feature to the replacement feature (if possible).

[ong6]

LGTM

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (17b3178) 45.66% compared to head (7c25f7f) 45.66%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2378   +/-   ##
=======================================
  Coverage   45.66%   45.66%           
=======================================
  Files         123      123           
  Lines        5199     5199           
  Branches     1097     1097           
=======================================
  Hits         2374     2374           
  Misses       2506     2506           
  Partials      319      319           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.