Say what you will, but using "google" is just the fastest way to say "search the web." Unless a better, equally convenient phrase comes along, it’s not going anywhere anytime soon.
I just "search".
I can't think how anyone is going to be confused and think I want them to check the bins or something, but maybe we search for different things on the web.
If you read the page, it suggests "to look up" instead of "to google", which looks like the same amount of syllables.
"search for" is just as short, and "search" is shorter.
They are actively transforming it into "ask Gemini" though. Which for me is often wrong. The organic search results are farther down, and if a lucrative term...you have to scroll past ads also. And the quality is not what it once was.
So Google is polluting what it means anyway.
To web-search (two syllables)
To google (two syllables, only slightly glibber, due to no "b-s" plosive-fricative combo).
Maybe "web search" can be shortened to "bsearch" or "besearch", like "web log" got shortened to "blog".
"besearch" has grammatical precedence: bestow, bequeath, behead, bewitch, belabor, befriend, ...