> Neither is the President who is actually elected by the Electoral College and not by a popular majority.
In this context, the electoral college is an implementation detail. American voters put a checkmark next to their personal preference for president, UK voters do no such thing.
> Regardless, does this even matter in terms of how politically powerful that single person is?
Yes, it makes a huge difference! The PM of the UK stays prime minister as long as they have the confidence of a majority of the House of Commons. The president of the US can only be prematurely removed if they are convicted of serious crime.
Voting is by name and election is by the Electoral College. The indirection remains.
No, House impeachment and Senate trial do not require a serious or indeed any crime. Impeachment is entirely a political matter akin to losing a confidence vote. It carries no penalty besides removal from office. Serious crimes and misdemeanors is not specified and drunkenness has been used (although it was around 1800 or so).
Regardless, does this even matter in terms of how politically powerful that single person is?