Is the android CustomTab API compatible with users privacy?

The CustomTab API is inherently fine and as noted allows the user to use a non-Chrome browser for viewing if that is their default. It also has the benefit that extensions work in them too afair, so if the user has uBlock Origin they get that benefit.

Regarding Safe Browsing:

  • in the WebView: works if GMS is available and SB is allowed in Play settings
  • in Chromium browsers: works if GMS is available OR if Enhanced mode is enabled
  • in Firefox browsers: works without GMS if an API key is available. Firefox, IronFox, Iceraven work. Fennec does not.

If you do use the WebView, you should set the telemetry opt-out manifest flag:
<meta-data android:name="android.webkit.WebView.MetricsOptOut" android:value="true" />

For this usecase of opening a link for a word, CustomTabs sounds like the best approach.