I think generally, unless you're really trying to be cost-conscious, hospital childbirth is all but a surefire guarantee to hit the OOPM. And if the birth itself doesn't hit it, the prenatal and postnatal care are usually enough to put it over the top.
Unless it's a horrible health plan, the only circumstance (apart from changing plans) where the OOPM probably isn't met with childbirth is if you have prenatal services in one year and then go into the hospital to deliver on or around Jan 1.
Really depends on the plan. When my kids were born my plan was ballpark $3k deductible, $6k OOPM, with 90% coinsurance after deductible. Pretty nice plan overall, relatively low expenses in the worst case, but the 90% coinsurance meant you needed to rack up $30k of medical bills after the deductible before hitting the OOPM. You can certainly exceed that with a more complicated birth or NICU stay after, but our uncomplicated births never quite hit that max. You'll definitely hit the deductible, but for the OOPM it will depend on the plan.
I guess I'm looking at it from a different perspective. FWIW, my view is skewed a bit by the plans available to me - there's less than $1k annual difference in premium cost among the 3 plans my company offers. Going into '22, our hdhp (middle tier) is a hair under $5k for the family premium, the "cheaper" one is $900 less and the "pricier" one is $950 more.
But regardless, suppose OP will incur $20k of medical expenses for '22, including birth, postnatal, and routine care. Probably not realistic but meh.
With the HSA, op pays $2340 + $3000 + $1700 = $7040
Family plan 1 is $4392 + $2000 + $1800 = $8192
Family plan 2 is $8592 + $1500 + $1000 = $11092
Even if all bills were somehow only $10k, op is still paying $6040, $7192, and $10942.
And if all bills reach OOPM, it's $8340, $8392, and $11092.
Worse, with the other two he they lose the offset HRA if they don't use it all. The only circumstance where OP pays more out of pocket is if they decide not to touch the HSA and then only plan 1 becomes a better cost (at the expense of free HSA money).
My point is, when evaluating health plans, assuming most tenants are equal, I just look right at the premium + OOPM and then figure that's what I'm on the hook for.
Some plans, I definitely understand, have different aspects (coinsurance being a big one) that would steer towards one or the other but in OP's case, there's virtually no circumstance where the HSA isn't the cheapest (unless they've read the plan summaries incorrectly)