Should be able to add a battery backup.

https://www.secamerica.com/how-to-add-a-battery-backup-to-an-existing-sump-pump/#:~:text=Luckily%2C you can in fact,pump using the Pump Sentry.

When it’s getting up to 92, is the air under the house still cooler?

I’d personally worry that even the smallest A/C unit you can get would be problematic in that small of a space. Might be worth air conditioning the rest of your house and unsealing the door instead.