You are quite right that in order to get back into government, you really do have to appeal to the widest electorate possible. And that is what Starmer has been trying to do.
But
@villain is also right in the Labour could pretty much say nothing and get back elected.
That says nothing about how good they are but how absolutely terrible the Tories are and have been. Certainly the worst government I can remember in my long life.
The 3 by-elections will confirm that.
I do have very mixed feelings about Starmer. He was probably the best of a pretty average bunch to become leader of labour. And he has turned labour round from the awful 2019 result.
But assuming they win next year, they will inherit a country that is in a desperate state.
And they will have to prioritise what they will have to do.
So don't expect much from them in terms of major changes because of that. Fact of life I am afraid.