Welcome to Android Central! The Home button on mobile Chrome only seems to be available on the versions that are preinstalled on non-Nexus/Pixel phones, and not on the version that you install from the Play Store. For example, my old Honor 5X came with Chrome preinstalled, and that version has a Home button. I also know that Samsung devices that use Chrome as the preinstalled browser also have a Home button. However, Chrome on my Pixel 2 XL and all of my previous Nexus devices did not have a Home button. I can't test it on my current devices, but I believe that if you have a device that didn't come with Chrome, and you install it from the Play Store, that version also doesn't have a Home button. I'm not sure why this is.
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