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there are two robots from googleThere's also the Mediapartners-Google bot that crawls for images, video and Adsense.
Do you need to submit something to google to tell me to index mobile pages?No, but keeping an updated sitemap.xml in your Google Search Console account [google.com] is helpful.
One for desktop and one for mobile called Googlebot-smartphoneHow old is this article?! Years ago, there were an assortment of UAs containing the element Googlebot-Mobile. The oldest ones--Samsung and DoCoMo--limped along until late 2016, but by then their primary mobile crawling was with an iPhone UA. But already in February 2014 they had dropped the “-Mobile” component of the iPhone UA string. Around April 2016 they changed over to an Android UA.
if you look now probably something like 80% of the crawling is with the Googlebot desktop and maybe 20% is with mobile with the smartphone Googlebot.