Power bank or power wall?

Sounds like you're looking for a power wall to run your whole house.

https://www.victronenergy.com/markets/off-grid/family-home#system-diagrams these are the guys I used 3 times now they are upper end of the market but it's far cheaper than batteries in a box while being maintainable (they are meant for the marine environment, guys on sailboats have to be able to fix things as sea).

The efficiency will depend on the specific gear choices and particular load it's not a single number. Passthrough efficiency will depend on if you want the full UPS features so you don't notice a blackout at all or can deal with a quick burp and that's still very load dependent (it's more a fixed overhead so is a smaller fraction as your load increases). For most scenarios your looking in the 90's.

Your missing a lot of details charging that bank from mains/generator/backfeed AC or via DC? They are all different and have design tradeoffs.

So my setup is solar on the roof inverter/mppt in the basement (You should never use micros on the roof prepper or not). First trade off string voltage/amperage vs wire gauge and distance, basically the higher the voltage the lower the wiring loss for that distance, as amperage goes down the the same power you can use less thick wire for for the same or lower losses. Conversely the MPPT the higher the voltage vs the battery setup the higher the losses. Finally the higher the string voltage the sooner your producing power and your voltages needs to exceed the battery voltages in nearly all MPPT's. Your goal hear should be 5% or less.

Now you have to get the power into the batteries, this is battery specific but generally mid 90's. Higher quality batteries have higher C charging rates and are more efficient (or they would heat up incredibly while charging at those faster rates you can buy lifepo4 that can recharge in minutes) they also tend to have lower lifespans. 5% here is normal so 100hw on the roof turned into roughly 90wh in the battery.

No discharge side my quatro 10k's are 96% efficient at peak so I'm getting 85wh or so of what came in from the roof if it went to the battery 90wh if it's direct to AC.

With raw solar panel prices down to $0.50 a watt it's doesn't matter much that's about 2c a kwh for 20 years at which point a typical panel is down to 80% of it's initial output and the MPPT's and Inverters will be on their last legs if not already replaced or repaired. Losing 10-15% I'm still so much better off than my $0.26 a kwh. Combine that with heat pumps and and my heating costs cheaper than buying in cordwood.