Can I clean the air filter by soaking it in gasoline and drying it?

I’m not sure , but you shouldn’t play with flammables if you are not sure what you are doing. We don’t want to see you hurt.

What is it clogged with, let’s start there?

Get a new filter if it is paper, and most lawnmowers have paper “accordion”.

Paper and gasoline NO NO.
If is foam, Dawn detergent and rinse it in water then let it dry and a little motor oil.

Change the oil while you are at it. I think it’s been overfilled or someone turned it upside down to clean it.

Foam filters for Briggs and Stratton’s are supposed to be wetted with engine oil, not soaked in it. Wash it out real good with soap and water, wrap it in a couple of paper towels and squeeze the heck out of it to remove as much water as possible. Then put about 5 to 8 drops of engine oil on it and allow the oil to soak into the foam, then squeeze it like you did after washing. Reinstall. Do not wash the foam filter in gasoline! It may ruin it. If it’s a pleated paper filter, replace it, no oil.