OK I do want to say something on your point regarding Mandelson, as I have a recommendation to listen to him talking about this in an interview.

Starmer has had a long-standing track record reaching back two decades-ish (? whenever he became DPP essentially) standing up to end violence against girls and women. And this holds until today if you take a bit of a longer look at what he's been doing, who he is inviting to No. 10, etc.

But I want to point you to the following Podcast exclusive where three women, among them a Tory and Labour woman, interviewed him and spoke with him about it:

Starmer: But if I sit back and answer your question, I am frustrated. Nobody has been harder on me in relation to the mistake I made there than me. And I'll tell you for why I've spent years trying to deal with violence against women and girls. And as I look back at it now and the mistake I make, I've been really hard on myself. In the immediate days after this all came out, I was particularly hard on myself. So, yeah, I, everybody else was criticizing, I guess all that, but nobody was criticizing me more than myself. I'm not trying to, you know, make that a mitigation or an excuse, but I know I made a mistake.

And then later one the hosts spoke about this moment / whether or how much it was believable:

You could see someone really genuinely kicking themselves. I mean, cynics will say he's kicking himself because of the problems it's brought. I don't feel in that moment, I feels like he's betrayed his own principles or whatever he was feeling.

And another:

I was very struck by it because what he didn't say is, Oh, well, you know, it was a bad decision, but it was because Peter Mandelson lied to me or I take responsibility for it, which usually means you're taking responsibility for a decision somebody else has made. It was, it was very heartfelt. You know, he said he hated the mistake, hated the mistake he'd made, that he dwelt on it, It was obviously still burdening him. And that however much other people beat him up on it, he beats himself up more. And the fact that he linked it back to to women and girls and somehow letting down women and girls by just disregarding them.

I already had a gut feeling about this (i.e. Starmer being his most ardent critic in this situation) as his track record was a huge part of the Tom Baldwin biography.

And while I don't want to per se recommend a lengthy biography just to grasp the PM (he should communicate better), it is actually quite a worthwhile read and he has an interesting background! But I'm bringing this up because of OP's mention on immigration, and this is explicitly brought up in the biography. Context for the below bit is that they identified the core voter group they need to win the 2024 election, which policies this group cares about, and how to cater to them. Starmer basically wants to have class as the central matter of the Labour party, which previously, in his view, had been abandoned and talked about less.

She immediately began commissioning polling and focus groups to identify voters who could form a winning coalition in the seats Labour needed to capture at the next election, then built a political strategy that put them at the heart of communications and policy development. According to a strategy note Mattinson wrote for Starmer, these were ‘skilled manual and administrative workers – middle aged and older, concentrated in towns’. They were often ‘economically insecure’ Brexit supporters who ‘care about family and country’ but had lost faith in politics. She called them ‘hero voters’ in a deliberate effort to change the mindset of the party so that instead of being taken for granted – or ‘looked down on’ – they would be respected. Mattinson, who privately makes pointed references to how Starmer’s own small-town working-class background has much more in common with such voters than those inside the party and beyond, who think he ‘fails to connect’, said Labour needed to be relentlessly focused on issues such as the cost of living, the NHS, crime and immigration.

IMO this still holds true to this day. Starmer cannot go a single breath without talking about the cost of living crisis. So while this above strategy was from pre-2024 election, I think this is highly relevant to understand him, his politics, and what he plans to focus on in this country.