Battery runtime

How long the bank actually carries the load — with the inverter losses people forget.

Result

Battery capacity200 Ah

Bank voltage12 V

Usable depth of discharge80 %

Load150 W

Inverter efficiency88 %

Runtime

11.3 hours

0.5 days at that load.

Usable energy in the bank

1,920 Wh

Actual draw including inverter

170.5 W

20.5 W of that is inverter loss.

Load you could run for 24 hrs

70.4 W

What this will not do

Run DC loads on DC where you can. An inverter idling to power a 5 W router can burn more in overhead than the router uses.
Rated capacity is measured at a slow discharge rate and at room temperature. Cold batteries deliver less, and lead-acid delivers much less at high current.
Tier your loads before the outage, not during it. Brain, router and one access point is about 30 W and should never go down. The cellar fan can ride.

The full build and the reasoning are in Chapters 40, 52 of the guide.