I’m not British so I might be off-base, but my understanding is that like other European parliamentary monarchies, the PM is the effective head-of-state but their title rests entirely on the good graces of the MPs who can (and often do) replace the PM.
Furthermore the Executive branch of government isn’t particularly powerful, unlike the US. Maybe I’m fundamentally misunderstanding things but I don’t often hear about a British PM spending billions or starting wars without parliamentary involvement, which US presidents regularly do even if they don’t enjoy a majority in Congress (which is not a situation that British PMs can find themselves in by definition).
Of course the UK has the problem of FPTP voting which leads to (quasi) bipartism which means the PM has a rather symbiotic relationship with over half of parliament, but it’s still a very different dynamic.