Google Phone app is finally getting the very basic Caller ID feature that will display caller’s name and number for all upcoming calls. The company has been working on the feature for quite some time now but it is now been rolled out to users on the stable version of the Google Phone app.
There are different versions of that app so call recording functionality depends on your phone. One thing that's confirmed is that if you record via Google Phone then it will always announce "This call is being recorded". MIUI EU versions still have MIUI dialer though which offers simpler recording options without announcement.