Is there any way to update domain NSes with API?
NameServersChanged_API can be used. However it does not change the NSes, as a result of the method execution the button
Change Name Servers to preferred appears, clicking on it results in the new, updated NSes (those that were set in API call) set in both BA and in the registrar (request for update is sent to the registrar). But there is no automated way to click this button for all the domains at once.