Is there any solution for deploying of site on wordpress with automated adding it to Google Search Console and Google Analytics via APIs (using html file for approving)? Sometime I need deploy up to 3-5 sites with routine operations like described above and it takes a very long time.
Google Search Console
Sadly, the Google Search Console API only allows you to check data. Nevertheless, keep an eye at Google Site Verification API. As far as I know, right now you can only get access to previously created properties but there's been a while since the last time I checked and they are getting new beta versions. Maybe in a while, you could manage everything through there.