does my apple watch use a search engine?

Hi

Yes, it does.

As part of the built-in features, under watchOS 4.x, depending on your location, Siri on Apple Watch uses resources including:

• Wikipedia - the encyclopaedia.
• Wolfram|Alpha - a computation search and knowledge engine.
• Bing Image/Video search engine.

More information:

watchOS - Feature Availability - Apple

Apple Watch does not include a Safari web browser. However, some third-party web browser apps are available via the App Store.

Apps that you may wish to consider include, for example:

• Squint Browser on the App Store

  "Squint works with TRADITIONAL WEB SEARCH ENGINES - Choose Google, Yahoo, Bing or DuckDuckGo."

• WatchWeb - The Web Browser for your Watch on the App Store

To browse and search for these and/or other third-party apps with the results pre-filtered to include only those iPhone apps that also include an app for Apple Watch, use the Watch app on your iPhone. Apps can be searched by keyword or app name via the Search tab.

Follow the instructions here to add and use compatible apps on your Apple Watch:

Use apps on your Apple Watch - Apple Support

A Search Engine is what you use to find websites in a browser. Google, Yahoo, Bing, those are search engines.

Since the Apple watch does not have a browser, there's nowhere for it to be using a search engine.

What exactly are you trying to find out?