In the present context, all the battery is going to do for you is get you a few minutes until the generator spools up and starts producing power. A battery system with enough storage to run even a partial household for a meaningful period of time is going to be huge bux.
Good friend of mine sells equipment to the data center market. Those guys run elite level UPS systems, because they can’t afford even a millisecond of outage. Their systems are all battery+diesel (mostly, some nat gas). If there is an interruption in mains power, the batteries carry them over until the diesels can get up to speed.
But unless you’re doing something pretty unique, you just don’t need that at home. And the difference between “backup system with zero downtime” and “backup system with 30 minutes downtime” is about 100x the price.
It always comes down to the old hotrod shop motto: “Speed costs money. How fast do you want to go?”
IMHO, the sweet spot for the average homeowner is a good quality gasoline powered portable generator. Like a Honda. If the time ever comes that you are going to need it, you will be relying on it to run continuously for days. You want something that is rated for continuous service. Keep it in the garage. Keep a couple of five gallon cans of gas on hand. If you happen to get hit with an outage, throw the main breaker on your box, drag the generator out to the driveway, plug it in (preferably to a 20A circuit if you have one) and be careful how many things you turn on in the house.
(BTW, if you go this way, a few times per year, dump the gas into your car and refill the cans with fresh.)
If you really want to step up you ice cold beer game, you can go to one of the stationary, natural-gas powered home backup generators. Nice and convenient, but a big jump in dollars, particularly since you need a professional electrician to install them. And they generally run on natural gas, so your power is only as reliable as your natural gas supply. Or you can get one that runs on propane, but that introduces a whole other set of supply chain issues. But even with those systems, you generally won’t get the “battery bridge until the generator kicks on” capability that the pro’s use.