Protecting the Mothership
The Oracle has taken you here for some currently unknown reason. You have lost control of the Mothership, although it can still construct things and conduct research. You have a fair amount of the time before the Hyperspace core is charged, but before that you will begin to be attacked by a new enemy, Progenitor Movers. Movers are Corvette-class but they boast pretty powerful weapons and a tough hull for their size. These will be the only enemies you'll face in this battle, so to begin with, invest in lots of Pulsar Gunships and Torpedo Frigates (further into this scenario, Fleet Intelligence will explicitly state that you should do this). Don't worry about the Movers being difficult to deal with at the start, they do get easier.
Once the Mothership has initiated its first short jump, begin moving your fleet along the path created by the dust strands near to where the circle is on the tactical screen; the Mothership will reappear here and will come very quickly under attack; if you don't protect it, the Movers will very quickly tear it down. When you get to this point you will be able to defeat two Movers to retrieve a derelict one which you can use to research Anti-Mover Weapons at the Mothership. Use a Resource Collector to collect it, then spend the RUs, and you'll find your weapons suddenly do a lot more damage to the Movers than before (previously a Pulsar Gunship squadron might have taken a while with each Mover but now they can destroy them in no time).
The Mothership will do another short jump and reappear close to a large derelict hulk at the edge of this place. This will be where it's moving to, so move your fleet up and defend it. This may take longer than any of the between-jump periods so you might want to build some Platforms to assist in its defence. Once it gets there, the Oracle will have obtained the information it wanted, will release its control over the Mothership's movement, and get the hulk to transmit an order to all the Movers to stand down. You can then progress further towards your goal of another Progenitor relic hidden in this region of space.