The aggressive marketing of Chrome on Google Search website to users using other browsers was a significant part of Chrome adoption success.
And no - some people didn't willingly and consciously switched to their search engine. It was pushed down their throats by browser vendors being paid-off by Google for setting it as the default one. Mozilla has overwritten user-changed search engine setting in Firefox with several updates.
Non tech-savvy users simply accept changes made in software they use.
Nowadays using Google Search is, since they pivoted from from being a "search company" to "adtech company" which resulted in the degradation of Google Search quality.
"Engines like Bing" is an ambiguous term. There are better options than Bing.
And no - some people didn't willingly and consciously switched to their search engine. It was pushed down their throats by browser vendors being paid-off by Google for setting it as the default one. Mozilla has overwritten user-changed search engine setting in Firefox with several updates.
Non tech-savvy users simply accept changes made in software they use.