I have once started to add checks for that in my CI/CD.
I used a self hosted instance of LanguageTool [1] (they also have a free API plan).
For checking links I used something self build. It checked all links (including in already published articles), archived them via archive.org and if they changed (e.g. offline) link the archive.org link.
After publishing, I also send the published article to archive.org and published links to social media platforms. Back then I also thought of publishing parts of the articles automatically to dev.to, medium etc. but never went through with it.