Russia sells oil to Iran in exchange for drones/etc, so they have very limited influence. China wants to break into the Middle East politically, which is why they were reaching out to the Saudis, so they aren't too keen on Tehran, either. Both Russia & China like that Iran is a major distraction to the West.
In my opinion, the problem is twofold: first, we are deeply enmeshed in Iraq and other areas due to ISIS, Iranian proxies, etc., second, we continue to allow Iran to fight a proxy war against us.
What the Biden Administration is doing right is pushing forward with the Saudi-US-Israel plan (defense guarantee for Riyadh with some nuclear power sweeteners, Saudi recognition of Israel for Tel Aviv, and the end of Chinese meddling in the region for the US).
In the meantime, we need to reduce our footprint in Iraq+, and speak Cuban Missile Crisis language to the Iranians: 'Any attack by Iranian proxies against US allies will be viewed as an attack by the Islamic Republic of Iran on the United States of America." Nothing more need be stated. The next attack, regardless of how trivial, gets a massive attack on Iranian naval assets in/near the gulf, including their submarines. Without hyperbole, without fanfare ("we are going to attack soon . . ."), just do it and let Admiral (ret) Kirby treat it like any other day.
As to the Houthis, President Biden et al bought into the "Saudis are the bad guys" refrain from the international left (newsflash: there are no good guys in the ME) and forced the Saudis to stop their campaign against the Houthis. I guess since the President had to swallow his "I'll make MBS a pariah" comment, he can choke down, "Sorry, my bad" and release the Saudis again. Of course, they'll want more support this time.
The Houthis are Shia extremists who support Hamas. We need to cut off their supply lines and stand-off bomb them. This tit-for-tat nonsense in the Red Sea is exactly what they want. We can impose an air and sea blockade of this desert entity (Yemen) and bring things to a quick conclusion, and one Iran will be unable to avoid. Of course, to do so, the administration would have to face the complaint that 50,000 Yememi children were starving to death a week/month/year, which will be about as true as Saddam's claims.