/usr/lib/xul-ext/webaccounts/content/browser.js that only loads the library
/usr/lib/x86_64-linux-gnu/webaccounts-browser-extension/libwebaccounts.so and calls it with info about the currently visited page.
webaccounts-extension-common that contains this library also has a file
/usr/share/glib-2.0/schemas/com.canonical.webcredentials.capture.gschema.xml that contains the gsettings configuration options of this package. There is only a single one, which lists the sites for which the extension was already active once and won't ask again. In my case, it contained
twitter.com, which is why I did not notice anything when visiting Twitter. This blacklist can be cleared with the following command:
gsettings reset com.canonical.webcredentials.capture dontask-accounts
The next time I visited Twitter, the Ubuntu Control Center opened with the Online Accounts dialog, so that is the desired effect of this plugin.
However, the source code of the library shows that there should be more. It contains a function
webaccounts_store_login that has the purpose of automatically adding the Twitter/etc. account you just used in the browser to the Ubuntu Online Accounts, such that the desktop integration just works immediately after you used the site once in the browser. This is of course a nice integration. However, this does not work for me (no account is added, only the accounts window opens), and there is a two-year old bug report that indicates that this is the same for others as well.