Google's John Mueller said if you still see that Googlebot Desktop is still the main crawler for your web site in Search Console settings, then you can try to "double-check the usual things to make sure your site is as strong on mobile as it is on desktop, for search & your users."
He added there is "no need to do anything special." I assume that means that GoogleBot will just switch over by itself when it goes to 100% mobile indexing maybe around September of this year.
But if you were not switched yet, that probably means Google sees issues between your desktop version and mobile version of your site. So you should do what you can to address those issues.
You can check your indexing crawler version in your Google Search Consoles settings over here.
Vintage Googlebot is visiting you, how cool is that :)
— 🍌 John 🍌 (@JohnMu) June 3, 2020
While there's no need to do anything special, I'd still double-check the usual things to make sure your site is as strong on mobile as it is on desktop, for search & your users.
Forum discussion at Twitter.