Passport services can get delayed by USA government shutdowns because various agencies have to coordinate to verify your identity and not all of them are fee-funded.
Ideally, you should have either filed expedited or gone to a walk-in passport office and pleaded for emergency same-day service. But it might be too late for that although you should try phoning the passport office to see if you can upgrade to expedited.
I think your next best bet is to hope that they at least send your naturalization certificate back as soon as they scan it. Then with that you can go to a same-day passport office and get one made same-day.
A more risky, strategy is to travel out with your former country’s passport, apply for an ESTA, and then when coming back into the USA show your naturalization certificate at US immigration and expect a nice haranguing at secondary while they yell at you for pulling a shenanigan. You can also
try entering through a pre-clearance airport in Abu Dhubai, Ireland, or Canada — or through the land border in Canada or Mexico. USA Immigration can yell at you and detain you while they check your status but they can’t deny you entry so you’ll get in, eventually.
Note: there’s evidence here on se of dual citizens getting ESTA. You should declare your us citizenship on the esta application in any case.