If Biden wanted to could he have people kill Trump since he is in office and SCOTUS said it was ok?

Nah, because he's a Democrat. SCOTUS would rule that was a violation of his presidential duties... they left that ruling incredibly vague so that they can be the authority.

You could argue that his oath of office requires it. But yes the Supreme Court only meant this power to be used by people they approve of

I think he could make a compelling argument justifying it if Trump were to win the election, a sort of Julius Caesar part deux. I think you could make the case that American democracy as we know it would end if Trump were elected president and that in order to protect democracy, his assassination was needed. However, in doing so, American democracy as we know it would still end because Biden would be opening the door to domestic political assassination being in a president's tool belt, so it's kind of a catch-22. We're damned if we do, damned if we don't. So really, the only thing that will "save" democracy is if people vote for Harris, that's where we're at as a country. I'd love to vote third party, I actually didn't care much for Harris before Biden dropped out, but the stakes are really too high this election to consider anything else.

To give a serious answer: The short answer is probably, the long answer is no.

The opinion was deliberately vague on that issue. A dissent said they could under Roberts' opinion, but Roberts calls that "fear mongering" without elaborating whether that's true or not.

It's also a pretty complicated opinion so bear with me. The whole thing comes down to this vague idea of official vs. unofficial acts which are supposed to be immune according to the court. Really, there's multiple factual allegations and the court said each one has some level of immunity (and if you think these are full of contradictions, I know):

• Asking the DOJ to pressure states to investigate obvious spurious "fraud" claims and pressure states to throw out their results, and threatening to fire them if they refuse - here Trump is "absolutely immune" because the DOJ is part of the executive branch and the president has power to fire them, I guess for any reason now.
• Trying to get Mike Pence to refuse the vote count and throw the whole country into a chaotic power struggle - presumptively immune, because the president and vice president can talk about their duties. Can be rebutted if the government can prove a prosecution wouldn't pose a danger of intrusion into executive branch functions, whatever the hell that means.
• Trump personally telling state officials to change electoral votes - here Roberts says there's no basis for Trump to claim immunity because there's no presidential power to try and coerce state officials. However, he then says it's up to the lower court to consider if it's official or not before proceeding, and is entirely unclear on who has the burden of proof here.
• Using twitter and a speech to organize and then start a riot at the capitol - similar to the above, the president has official duties relating to speaking but yada yada yada it's sent back to the lower court to decide whether this is official or not.

Conclusion: Ordering an assassination of a rival certainly sounds most like the first - the president has several official duties relating to giving military orders, and the military is part of the executive branch. The FBI is also part of the DOJ, so if Trump can order the DOJ to do something criminal, that itself could be an assassination. But as described in the article below, one could make an argument that no, the opinion doesn't actually say he do that with the military specifically, because congress has some powers relating to war (not convincing). However, to be fair to that opinion, this immunity ruling is such a stinker that lower and future courts will limit its holding as much as humanly possible. Plus seemingly contradictory aspects to it (Trump can order the DOJ to do things he can't do himself?) could be used to argue for exceptions to the overall immunity. But reading the opinion at face value, yes the president could order an assassination, and even fire generals who refuse to pass along those orders.

Longer answer though: This is the real world. If Biden gave such an order, it would likely result in a coup and an overthowing of the Constitutional order as a whole. And if order were somehow restored and Biden brought up on criminal charges, you could be your life that the 6-3 Republican majority on the court would find a way to either limit or perhaps overturn their prior ruling as it pertains to Biden.

For an alternative perspective on the same topic, here's a center-to-slightly-right-leaning law professor's take on this which does a pretty plausible job sane-washing the opinion.

If it's an official act, yes. It's not hard to tell a story where it becomes an official act. I I think he could still be impeached FWIW.

Because of Trump's unhinged tactics, we know that top military leaders and (presumably) TLA bigwigs have discussed what they would do in situations like this. What you're describing is very close to a coup d'etat, and in a situation where they get ordered to perform such an action, do they do it? What was framed as a question of SCOTUS rulings becomes, in reality, the question, "Am I willing to throw this entire democracy away on this President's absurd orders?" Every high-up in government knows this... They signed up to serve the people, not a dictator.

Of course we have no idea how each person would act, but my point is that pure legality is only one challenge Biden would have to overcome if he wanted to do such a (horrible) thing.

The question really is whether or not the assassination would be an official act.

they left it to 'congress' to decide what is and isnt an official act. so, congress being run by a bunch of conservative morons would indict biden but let trump walk for the exact same behaviors.

It would be incredibly stupid to assume they'll play even by their own rules. They're just voting that because it was enough to buy Trump time and leave everything "up to interpretation". It's not like it was going to help Biden in the short term like it did Trump

No, he cannot legally, because it would be a corrupt and partisan SCOTUS deciding if that is an official act.

I mean yes, but more often than not, people generally DON"T wanna kill other people

He could not be prosecuted for it, but my understanding is that the people who killed Trump could be prosecuted because it's still a crime (it's just that Biden can't prosecuted for it)

Except, he probably doesn't agree with that scumbag ruling. I'm pretty sure if he did the supreme court would reverse course on it. Its not like they have any integrity.

If you start with the answer you want to get and "find" the construct the law thereafter you can find anything. You can even find one thing one day, another the next, and yet another the day after. The supreme court is a Republican tool which has little legitimacy.

They would find for their side wherein they reasonable feel it won't harm them or the future or trespass beyond their own personal opinions not on what the law says but what they think it ought to be.