My (not-a-lawyer, not-a-Constitutionalist) understanding is that basically nothing has changed. It has always been understood that you can’t criminally prosecute a president for “official actions” - doing something that’s considered within the scope of his duties, such as waging war on an enemy nation or issuing an executive order permitting oil drilling on federal land. The only real/legal check on a president’s power in doing such things is impeachment and removal-from-office itself. That was always the case before this Supreme Court decision and remains so afterwards. The Supreme Court merely formalized this as a rule.
However, “unofficial” deeds remain totally prosecutable. If a president tries to pay the mafia to take out some political rival or embezzled a lot of money while in the White House, he could definitely face criminal charges for it. That, too, was always the case before this Supreme Court decision - and the Court merely formalized it.
So, to answer your question - no, nothing has changed. What’s “official” is protected, and what’s “unofficial” is unprotected.
The problem, though, of course, is that it is going to become maddeningly difficult to define what exactly is and isn’t “official.” It may take decades of litigation to sort that one out properly.