A sewer backup in a basement is contaminated water and it is handled differently from a clean water loss. Porous materials that have been in contact with it come out rather than getting dried, because contamination lives inside them where no cleaner reaches.
The first job is stopping the flow, which means clearing the blockage or establishing that the main is surcharged and nothing more will come in until the storm passes. Everything else waits on that.
We handle the plumbing side and coordinate on the restoration side. Carpet, pad and drywall below the water line are not salvageable after category 3 water, and anyone telling you otherwise is not doing you a favour.
Technician insight
Do not run water anywhere in the house while a basement is backing up. Every fixture used adds to what is on the floor.