There's a mixed response to this on some political commentaries on youtube. With some saying it'll backfire on Starmer as polling suggests that Reform will take the by-election seat, unless Burnham is the Labour candidate. Or even possibly the Greens, possibly putting Labour in 3rd place!
But, Starmer appears to have been in a no win situation, as despite his bullshit about 'the people of Manchester do not want to be inconvenienced with another mayoral election', polling suggests that it does seem likely that if Burnham had vacated the mayorship, then a Reform candidate may have won the mayorship of Manchester!
Some pundits are having a dig at Burnham, others having a dig at Starmer.
What seems clear is that Burnham's personal popularity has been increasing, (with an increasing share of the vote for his second mayoral term,) but this is most definitely not the case for the Labour party as a whole, and specifically Starmer himself is extremely unpopular.