This feature should be back in the upcoming weeks while Google makes infrastructure changes.
The announcement. Google posted this announcement on Twitter:
Normal indexing unaffected. Google said it will continue to index sites through normal crawling and indexing. It linked to this developer document on how Google crawls and indexes the web.
But you currently cannot use the Request Indexing feature in Search Console to push content to Google Search.
John Mueller of Google clarified this on Twitter:
Recent complaints. There has been a lot of complaints recently, mostly stemming from the ongoing indexing bugs, around Google not indexing content quickly enough.
Why we care. A lot of SEOs have been using the request indexing button during the past few weeks while Google has been having indexing issues. It is their way of pushing content that Google is having a hard time indexing, into Google’s index. Maybe we are over doing it and Google cannot handle the load? Maybe there are other bugs with indexing where Google had to shut this down? We are not sure.
It will come back — until then, you cannot push content to Google using the Request Indexing feature in Google Search Console.