Question about planned c-section cost – how Childbirth lump sum allowance is actually applied

Hi all,
I’ve been trying to understand how the Japanese Childbirth Lump-Sum Allowance (¥500,000) apply in practice for C-section costs.

This is my basic understanding and I don’t know where insurance applies actually.
1. Hospital bills total childbirth cost (surgery, hospitalization, etc)
2. Direct payment system applies Childbirth lunp-sum allowance to the total childbirth cost at discharge
3. If total cost < lump sum → receive the difference refunded by insurer
4. If total cost > lump sum → pay the difference at discharge

I will have a planned c-section, and my hospital in Tokyo provided me that c-section cost will be ¥700,000 (excluding private room fees). Hence, with my calculation, I will surely have to pay ¥200,000 out of pocket plus private room cost. However, in some Reddit threads, people shared their experience that they even got refund from c-section sometimes. To my knowledge, most of the c-section cost in Tokyo are in similar range with my hospital.

So what I’m trying to confirm is:
Does the ¥500,000 lump-sum grant get subtracted from the hospital’s entire bill, or only after applying the insurance 70/30 split to patient share of hospital bill (excluding private room cost, meal cost etc.)?

Any explanation from c-section experience would be really helpful.

TIA!