Notes in case it is converted to an HTMLForm first:
To add more sites client-side:

var addMore = OO.ui.infuse( $('#mw-input-wpsites--create') )
addMore.$button.trigger('click')

and then set the field values accordingly

Thinking about this again, given that outside of a one-time migration at the start the need for this should be pretty rare, adding the functionality to the user script version to just set the options via the api directly might be a better idea

In T258770#6375100, @DannyS712 wrote:

Notes in case it is converted to an HTMLForm first:
To add more sites client-side:

var addMore = OO.ui.infuse( $('#mw-input-wpsites--create') )
addMore.$button.trigger('click')

and then set the field values accordingly

It was indeed converted to an HTMLForm

In T258770#6477437, @DannyS712 wrote:

Thinking about this again, given that outside of a one-time migration at the start the need for this should be pretty rare, adding the functionality to the user script version to just set the options via the api directly might be a better idea

But we no longer have a dedicated api

At the moment, given the differences between the user script version and the extension, and the fact that the script will still work, leaning towards declining this and just adding an alert to the script telling people that the extension is now available and that they may want to use that instead.