The EU (Withdrawal) Act 2019 does indeed only mandate the PM to seek a further extension, and says nothing about the aftermath. In fact, the only sections that focused on the possible aftermath were removed from the bill.
In the event, the motion it forced the government to table has merely given Parliament a chance to vote on the 30th June exit date (passed by a 310 majority as a type, the ERG presumably voting against), which is rather disappointing, because (a) Theresa May had already proposed this date (twice), and (b) that rather defeats the point of having this Act in the first place, which I had understood to be to hand to Parliament the question of whether or not to request a further extension. In pre-empting the Bill's passage into Law, Theresa May has again acted rather shamefully, although in refusing to suggest another date, Parliament has again merely enabled this.
Still, at least this time there can be no meaningful doubt as to the legality of requesting a Brextension, as statute has been created to force the PM to do what she could probably have done anyway, by executive powers.
As to what happens afterwards: more likely than not, the EU will offer some flexible terms to allow for whatever time the UK needs to get its act together. If it does not, it should be abundantly clear that the will of Parliament has been to reject a "No Deal" exit. Therefore, do not be surprised if legislation is once again rushed through over Thursday and Friday, giving the PM the power to revoke Notification.