Sorry, I had that happen too. During superstorm Sandy. I couldn't get to a generator for a couple of days, either. Lost some appliances and water heater, but the furnace was spared. Moved a couple of my favorite pins out of the basement when it climbed to 8" deep just to be safe.

Anyways, once I got the water pumped out: fans, fans fans! ...and dehumidifier. Get as many fans and dehumidifiers going as quick as possible. If you have drywall, cut around 10" up from the the waters high level and rip that out. If you've any carpet, wood or wood particle board shelving, boxes, or anything that can soak up water get it out of there. Squeegee, vac and mop out any standing water. Like they said, just keep drying it out for a about a week. We did not have to replace the studs, sometime a month or later we repaired all the drywall.

That is not a flood. That is a little water. Get out some fans and a dehumidifier.
Mine was 8" deep. Half of your carpet is dry.

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When Sandy flooded our house, we lost a lot - appliances, water heater. Luckily, at 10 inches deep it missed the control panel of our new furnace. We have a sump pump rider on our insurance that covers the water heater and other appliances. It doesn't cover things like non permanent bookcases and shelves or other contents.

As a preventive measure - the gutters had issues on the back of the house, so we had those all replaced. I also bought a generator of my own. We had foundation problems with bowing and leakage, and had the entire back of the house excavated last year: walls straightened and I-beamed, waterproofed and correct drain tiles, the backfill is to the surface with gravel. I wanted to mention that because things such as poor gutters and exterior drainage problems can exacerbate flooding.

Sorry you had to go though this.

While we're on the subject of floods:
https://papa.org/about-papa/papa-flood/