Not very often I agree with you, but I think you are right on most things here.
I think you are wrong on a couple of details: he wants to be perceived in the short term as a compassionate conservative, and will implement short term policies to that end, for the simple reason that that perception will get him through to the GE and, based on a record over a two year period, probably a landslide. at which point he will be able to implement the things he truly believes in, which constitutes an ultra libertarian capital economy. Small hands off government, ultra privatisation, Low regulation, low tax for capital: and low wage, low protection, relatively high tax, and significant policing of personal lives for those who actually work.
The stuff about Braverman does matter because ideologically she is in genuine extreme authoritarian territory, with everything that implies. Today its shipping immigrants and asylum seekers to Rwanda, and limiting / removing the right to protest - which rights tomorrow does she want to remove; free association, Independence of the judiciary (which is teetering on the edge as it is), additional police powers. The right to trial.
KS and Labour have to start thinking long term or at least medium term, but I think the nature of Starmer is that he's someone who thinks he can win an argument at PMsQT at which point he's won and everything is suddenly fixed.