There will almost undoubtedly be a swing to Labour in the next election. However, I don't know what the predicted swing is in individual seats, but I suspect Starmer does. The swing won't be uniform and will be affected by Labour voters who don't think Starmer is left enough and votes for Reform and those who won't be bothered to vote.
If you look back to 1979, Thatcher didn't win that election because she promised a right-wing agenda, but she promised competence as opposed to the muddle and weak economy which had characterised late 1970s UK. The "Winter of Discontent" persuaded some people that the unions were in control. Callaghan was seen as weak and Thatcher impressed people with her single-mindedness. Her pledges to control inflation, immigration and promise to introduce "Right to Buy" won over enough former Labour voters. Whilst promising to control inflation, she didn't actually say that much about public spending, benefits or tax. Like her or loathe her, she a lot of charisma.
I'm sure Starmer has sat down with his focus group leaders and strategists and has had feedback about what people actually want at the moment. I suspect that they want a strong leader with a plan to improve the cost of living, the NHS and education. They probably would like somebody who appears relatively honest too.
I don't really know what his game is, but I suspect very strongly that he has one. Starmer needs to make sure that his votes are in the right constituencies.