The biggest problem for European countries is not oil in the first place, because they can pressure producers to increase production, including Venezuela. The great crisis in the Russian invasion with the approach of winter. Gas is Russia's trump card in this confrontation.
Relations between Iran and US are not warming up. Rather they are getting worse by the day. And Iranians are used to sanctions and at this point they know that the Western nations want them to increase the oil and gas production desperately. Since they are under embargoes for such an extended period of time, I really doubt whether Iran will be in a hurry to get rid of them. Especially given the perilous situation many of the Western economies are in. And increasing the oil production will also mean driving down the market price. This may not be acceptable for them.