A very good result for Burnham. Winning over 50% of the vote on a turnout 6% higher than the GE is quite some achievement. Normally by-elections have very low turnouts and the governing party gets hammered.
Good work by the electorate to align their votes behind Burnham with the LDs and Greens mustering less than 3% between them. I didn't follow the campaign in any detail, but it's suggestive of antqcit understanding between the local Greens, LD and Labour whereby they didn't campaign too hard. We had a similar unspoken agreement down here in the GE where Labour left the LDs a clear run in Wokingham and the LDs allows Labour a clear run in Woodley & Earley. I'd hope this represents a path for future cooperation because in my view stopping Reform is more important than anything else.
The popularity of Burnham in the area also seems to have contributed to the result.
Anyway, I suspect it spells the end for Starmer. The first obstacle for Burnham has been easily negotiated despite a lot of doubts about whether he could win the seat; losing would have been politically disastrous for both Labour and Burnham (although obviously not for Starmer). The next obstacle is getting enough Labour MPs to trigger a leadership contest: I don't see this as an issue as Starmer has pissed off more than enough of his own MPs.
Statmer's inability to do politics will now be his downfall. The early missteps including u-turns, tentative government and hardline discipline will result in the threshold for a leadership election being easily reached and polls of Labour Party members show Burnham comfortably beating Starmer comfortably. Hopefully it'll be enough to stave off Reform, but the problems remain and there would be under 3 years of the parliament left.