Due at the end of month, go with COBRA or new insurance?

I am due at the end of the month and we currently have two options for insurance – COBRA and insurance through my husband's new employer. We lost coverage from the old employer on September 28, and because we had already met the deductible and we know everything between now and delivery will be covered, I was hoping that we could do COBRA for this month and then start the new employer's insurance starting in November. However, turns out that if we sign up for the new insurance within the 30 days, coverage is retroactive and according to Google, you can't have COBRA and another insurance (and even if you can, I don't believe COBRA can be primary).

Because we only have a couple months left in the year, I don't think it's worth it to get the new insurance for this year as the options are only for a high deductible plan, but COBRA will also end up costing around $3000/mo. with the new baby. Has anyone been in this situation before? Would it be worth it just to go with COBRA since we at least we know we literally only pay the premium whereas with the new insurance, I'm not sure what/how visits are covered. What would be super helpful is if we knew exactly how much the delivery/pediatrician visits cost, but I know that insurance is billed differently than if I didn't have any insurance.

How does retroactive insurance even work? Do we pay for all the appointments/delivery out of pocket and then file with insurance when we have it?