Labour's basic problem is that it's not just unpopular, it's unpopular with different sections of the electorate for sharply opposing reasons. So it can't solve either one of its unpopularity problems without making the others even worse.
A bunch of centrists, soft Tories etc. were just persuaded to hold their nose and vote Labour at the last election because the Tories had gotten so catastrophically awful that noone could pretend they were serious candidates for another term. These people expect reasonable continuity, a responsibly managed capitalist economy without the rampant incompetence and corruption of the Tories.
Some of these people reacted badly to what they saw as early missteps such as raising employer NI contributions. The problem with trying to satisfy them is that capitalism IS failing due to global factors far beyond the control of the UK Labour party. And also the fact that they are not long term, natural Labour voters in the first place so are unlikely to stay on side if the Tories can even slightly get their act together. I doubt the choice of leader makes much difference here.
People on the left were split, with some in marginal seats voting Labour despite being underwhelmed by their offer, but many others having given up on the party already - particularly as Starmer had shafted them in his leadership bid and then made such a show of expelling many from the party. With the Greens ascending, these people now have a practical alternative they didn't have before. And Labour has lost its capacity for including left wing perspectives within policy development.
The antipathy of this group to Labour is very largely personal, centred on Starmer, and there's nothing he could do as leader that would unburn those bridges now. Burnham might help, a bit. Streeting certainly wouldn't.
Then you have Reform voters, some of whom are ex-Tories and some ex-Labour (red wall etc.) now with a visceral hatred of Labour who they see as having betrayed them. There are socially conservative issues at play here that are pretty much impossible to square with the few remaining areas of loyalty Labour has left, among educated youngish people in cities.
A lot of these people are pretty immune to reason or analysis, are deeply attached to a victim mentality and there is NOTHING Labour could do that would satisfy them and get them onside. But there's a lot of them and they make a lot of noise, and possibly for this reason Starmer has put a lot of effort (in terms of comms and rhetoric, at least) into trying to win them back, at the expense of the other two.
This has been a spectacular failure and a demonstrable error of judgment on his part. I don't mean failure because I don't like it or the Labour party should have different priorities - I mean failure because it hasn't worked. For this reason he should probably resign. When political leaders spectacularly fail they generally resign, or at least they used to.
As for who takes over and how they square this circle, God knows. I can't think of a job I'd want less.