The US president has far more power than the UK Prime Minister, who only leads their party and requires MPs to vote for anything they want to do, as Boris Johnson discovered last year when he failed to get his plans through parliament multiple times.

Far less. Yes, the PM can fail to get a bill passed by his own majority and can even lose a confidence vote. But the President can’t even submit a bill to Congress, and then either or both houses of that Congress can be of the opposite party. Even the Senate can kill legislation or appoints by failing to reach a supermajority over a filibuster.

Perhaps less (or similar) lawmaking power, but the President of the US leads an entire branch of government which comes with a significant amount of power in its own right.

The President leads the Executive Office of the President. The Federal agencies (the Treasury Department, Department of Defense, ...) are themselves led by Cabinet Secretaries nominated by the President and confirmed by the Senate. The Prime Minister appoints Ministers not subject to confirmation by anyone else.

You are about to see how important this confirmation veto is.

The prime minister of the UK isn't directly elected.

Neither is the President who is actually elected by the Electoral College and not by a popular majority. States matter A LOT.

Regardless, does this even matter in terms of how politically powerful that single person is?

> 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).