There seem to be three main 'camps' on the Burnham question on Bluesky:
1) Starmer loyalists. To them, Starmer was brilliant, soon to be granted sainthood, with a flawless political sense, and a clear way to win the next election. Everything was going fine, and any upturn in the polling is totally down to Starmer. Burnham is a dirty rotten scoundrel who had been plotting for years, and is now just riding on St Keir's coattails.
2) Corbyn-type loyalists, for whom any concession to trying to work with other parties or a system they see as a capitalist conspiracy (well, they might have a point there) is a complete sell-out to capitalism. What's beyond the pale to them is using 'retail politics' to try to gain back left-centrists who have drifted off to the Greens or Lib Dems. It's gotta be pure, or it's undisguised capitalism.
3) Pragmatic left/liberal not-racists who's attention has been caught by the small but quick announcements, which suggest (maybe falsely) that Burnham is going to deliver the 'reset' that Starmer claimed he was making but then utterly didn't. For them, time will tell, but they are sending a message that Burnham deserves time to try.
If the polling trends are to be believed, the third group is drifting towards Burnham and taking people with them, with no great enthusiasm yet, but with a semi-optimistic "Let's see" approach.