Backup house power via Inverter/charger & batteries

[Cujet]

If I got an inverter that is 4000 watts and uses 48V input that means it will pull 90 amps from the battery if I was using the full 4000 watts. Can a 48V 100 AH deliver 90 amps? Even if only for about 1 hour.

Short answer: No.
Longer answer: It depends on the battery you choose and its BMS as to whether you can even draw that much from it for a few mins.
Correct answer: Discharging a LiFePO4 battery at 1C (depleted in 1 hour) is way too much. The correct discharge rate is no more than 1/5th C. A 100AH battery 'likes' a 20A discharge.

Note: The AH rating of the battery also is probably a 20 hour rating, a healthy 100AH bat can produce 5A for 20H.
A 100AH LiFePO4 is not at all likely to produce 100A for an hour regardless of brand or price.