More than you think. They are also actively seeking ways to make that leverage effect more people.

They are defining web standards. They control chrome and chromium. So all of the alternative browsers that aren't safari and Firefox are using Google's web engine. Even Firefox and safari are beholden to Google as they fund both these web browsers through their default search deals.

Google after many failed messaging apps has taken on RCS messaging. They provide most of the supporting infrastructure through their Jibe servers. They don't allow anyone but themselves and Samsung to make an RCS app on android. They also had a campaign to pressure apple to use RCS. It's likely apple's RCS will be following Google's Jibe service closely, as they've already said their will work with Google on this. Google successfully got most RCS messages going through their servers, with apple on board with RCS itll see most SMS messages defaulting to RCS and most of those going through Google.

They also have deep hooks into education market with their OneDrive/Google docs products and Chromebooks.

Most privacy focused android alternatives recommend Google hardware.