Very, very little.
Just like Trump had very, very little to do with gas prices during his administration and same with Obama.
This isn't "my own little world", it's reality. Not everything in the world revolves around the presidency. Your doublespeak is so apparent. When it was Obama, you claimed that he couldn't stop oil production because it was on private land. When it's Biden, you claim that he is suppressing oil production because of public land leases (which even if it were true, for you to be consistent you'd at least admit that this is a minor factor).
What's obvious to anyone who doesn't have end stage partisan hackery is that oil production took a nose dive when demand took a nose-dive. Ramping production back up is slow, and oil companies aren't excited to pile in a lot of money if the price just drops again. They'll ramp up slowly, enjoying the profits from high prices, and bracing for the next shut down.
The market isn't stupid. It's just that the story is more complicated than what you're going to hear on the media that treats you (and everyone else on the right wing) as a moron because you're more useful that way.