In addition to the downsides mentioned here about privacy regarding Google, there is a major upside to using this service: it offloads all of the authentication logic to google, so in theory it reduces your risk surface area, or it may be more accurate to say it concentrates your risk to your Google account.

You’d like to hope most websites use using common security best practices and keep on top of things but the amount of websites I had accounts on (on websites I had long forgotten) which have been pwned over the years tells me otherwise. Using google auth sets your account security to be exactly as secure as your Google account.