Clearly you can't separate "Presidential" immunity from the ordinary type of immunity.
Presidential immunity does not cover crimes committed outside of the duties of the office of the President. If the President pulls a gun and shots someone, he is not immune from being prosecuted for that crime. If the President, while is was not the President, engaged in a criminal money-laundering and influence peddling scheme, he would not be immune from prosecution for those crimes. If the charges arose while he was serving as President, the House would decide whether or not to impeach him - it depends on if the crime were on-going as this one with the Biden crime family seems to be - and then the Senate would need to convict. Otherwise, the criminal prosecution would have to wait until the President left office. So, the silly "hypotheticals" used to strip Trump's Presidential immunity are irrelevant. As a President, he would never have been immune of the crime of murder - except as it related to his Presidential duties. The closest we've come to this conundrum was with Obama ordering the assassination of American citizens - which he is SPECIFICALLY NOT authorized to do by American law. If a President orders the military to kill a terrorist, that wouldn't be a crime that he could be charged with once he left office. The World court at the Hague might see things differently. But not US law.
Stripping Trump of the lawyer/client privilege awarded to ALL citizens was just plain wrong and I promise you, it WILL hurt Biden once he leaves office and it will hurt every subsequent President. Stripping Trump of the presidential privacy privilege which allows him to talk to his advisors without having to worry about them being pulled into court to testify against him was just plain wrong and I promise you, it WILL hurt Biden and all subsequent Presidents. If the President cannot talk to his staff with the assurance of privacy, he cannot do his job and if you think he can, then I'm sorry but you are an idiot and it's a really good thing you will never be the President.
If we were to allow Presidents to be charged with crimes because we didn't like their policy or the outcome of some action, every President would be hit with a rash of lawsuits once he left office and spend the rest of his life in jail or defending them. Every President who has ever served this country has made some mistake that others would love to be able to "punish" him for.