There is no scaling, it just happens sometimes.

If you go back to the last saved game, it may not even happen again.

Ironically, I was playing last night, and just before my final mega invastion the pirates showed up.  I captured the remaining enemy planets in one turn, and the game was over.

This is an equalizing event.  If you get it, you can reload from previous autosave, or choose to play through it.  Say goodbye to all of your ships and starbases - fortified trade routes will survive.  I would sell or scrap every ship immediately.  As mentioned, the only thing you can do is invade planets with fast (or carefully moved) transports.  You could consider upgrade some of your ships to transports that aren't in immediate danger.

Ascertain the pirate's weakness, research/trade techs/logistics/miniaturization to make fleets simultaneously.  In the meantime, don't make any ships at all, unless you have an opportunity to invade with transports.  Otherwise, set miliatart spending to zero.  This may take awhile, but the turns will be fast.  The AI will never recover from this, so its almost an automatic win when you recover.

I had this happen in my current game, and the Pirates promptly sent every race in the game back to the stone age, trapped on their worlds. My medium sized ships, at the time perhaps the strongest in the game, didn't stand a chance. It was dozens of turns biding my time while my new Destroyer fleets were designed and constructed.

The first few versions were wiped out as well, but model after model, my warships started taking more and more Pirate vessels down with them, with the finally victorious design boasting a vast array of shielding and multiple mass driver weapon arrays. The other races have fared even worse, and my new, ever growing Destroyer fleet designed specifically to counter the Pirates now stands uncontested in the galaxy.