Browser2 is a copy of the WebViewShell, a minimal test browser using WebView. The old Browser is no longer supported.
This is not a production quality browser and does not implement suitable security UI to be used for anything other than testing WebView. This should not be shipped in production devices, or used as the basis for implementing a real browser.
To build a full-fledged browser for AOSP, one option is to build a standalone (non-WebView-based) Chromium browser by following the instructions at: https://www.chromium.org/developers/how-tos/android-build-instructions