@eco-g
I think this is where we have a fundamental difference of opinion. If your goal is to grow the GPEW across the UK, then you are probably correct. Though if the results end up being a Reform Ltd victory, Labour a close second, and Greens winning enough votes that they're blamed for a Reform Ltd victory then I can also see that backfiring and causing a lot of nation-wide resentment towards the Greens.
But if your goal is to shift the Overton Window to the left, combat the rise of the far right, and increase progressive policies being pushed in government, then it's exactly the wrong strategy. The best outcome for this is that Burnham takes a seat, wins the Labour leadership, and has a few years to show that progressive policies help people before the next election. Labour can then enter the election on a message of 'look, we're working for you!' and the Greens on a message of 'look, that stuff worked but was too timid, let's do it even better!'.
I don't see any chance of Labour or the Greens winning an outright majority in the next election. But I do see a path to them winning enough seats between them to be able to govern (whether as a formal coalition or one of them as a minority government). If you want that, then helping the left wing of Labour reshape their party into one you'd be willing to collaborate with is a vital part of your strategy.