Neither Dems nor Orange have that much control over gas prices. Their most powerful switch is releasing from the strategic reserve.
Permits for new drilling lands are not impacting gas prices that much. That already have plenty of unexercised existing permits.
Oil is a global commodity priced at a global level. Pretty much every other nation is seeing the same rise in fuel prices.
People keep associating has prices with presidents. It's rather strange. If gas dropped to $2/gallon over the course of the next year it would be extremely unlikely to be Biden's doing.