The ruling is vague enough that any specific cases can be decided based on the court's political preferences.

No, he can't. It would turn out that isn't an official act, because reasons.

So, kinda. The ruling did have more nuance than a lot of people take from it, but it's still not a good ruling by any means.

The president has absolute personal immunity for core constitutional acts, and the presumption of immunity for official acts.

That means that you can't sue Biden for vetoing a bill, or other things defined in the constitution. That doesn't mean you can't sue the office of the president, but that you can't sue the individual.
The next part is that the courts need to assume that there's immunity for anything done "as the president" unless the prosecution can argue that not having immunity couldn't possibly infringe on a power of the president, and you can't use the presidents motivation to make that case.

So the president talks to the justice department about what they can do to sway the election for him: you can only talk about the impact of holding the president liable for talking to the justice department about elections.

You can't talk about the president assassinating a political rival because that introduces their motive. "Would the office of the president be hindered by holding them personally liable for using the constitutional power to command the military to target a threat to the country".

Trumps family could sue, but Biden wouldn't be liable, only the executive branch.

The entire point is that Biden won't, though. It's just more of the rules for thee, not for me shit that fascists love.