"Google" is a company built on a search engine. It isn't a verb.
In 1998 Larry Page wrote in an email "Have fun and keep googling!". It is the first recorded usage. Of course he would would want you to use it as a verb.
But when you use "Google" as a verb for "search the web", there is a problem. It builds into language an assumption that Google is the One True Search Engine. There can be no other web search engine, because the word for "search the web" is Google.
That isn't true. Google is a good search engine, sure. But it isn't perfect for every search every time.
I use DuckDuckGo. It has a better privacy story and tooling. Microsoft Bing has a rewards program. Wiby Is a search engine for "classic" websites. Wolfram Alpha will give precise information that you won't find on Google.
Search engines are amazing modern technologies we didn't have two decades ago. They shouldn't be shouldered out by language. So the next time you tell your friend something you looked up with a browser, let them know you searched the web for it.