Which seems reasonable on its face, but it faces another issue. Now, what defines an 'official' act as president. And how loose do we want to play with those terms. If we want to play slippery slope, which is what the court seems to like to do, then something that should be illegal but can be deemed an official act is a President ordering the military to keep voters out of voting locations because they have a 'tip off' from someone in national security that a potential terrorist attack may or may not happen at voting locations. Right, we can end up in a situation where the president can find any loose way to justify anything they do.
That is where probably the blanket immunity comes into play. Its not definitionally blanket immunity, but it might as well functionally be blanket immunity.