And yet when you address President Obama he is still President Obama and not former President Obama.... Same as it has always been for President Bush or President Carter or President Clinton

There's absolutely nothing out of the ordinary about this.

the only thing even slightly strange is that normally in that context you would use the former tag, but it is still absolutely normal to address them as President in all cases and as a former in some. That's what happens after you earn that title... Doesn't mean you were a good President, it just means you were a President.