I don't think Starmer's history there is a major factor either way in politics in the large, though he did choose to raise it in the same statement. It would require significant qualification for him to go against it. I just find it repellent the way he attempted to manage, and effectively to quash any substantial support from his side of politics for a necessary justice movement.
We know the one big underlying reason why Labour got hammered at the last election, its base was fundamentally split on Brexit. Corbyn couldn't advocate for Remain or for Leave without suffering huge damage, and equivocation was no better.
That split wasn't a solvable problem, but nor is it one that can be charted back straightforwardly to disconnected middle class urban activists, etc. The effect of that "ground game" turns out to have been significantly overstated after 2017, anyway—perhaps it was more about an atmosphere reflecting the potential for change that time.
But that split is also not a problem that necessarily persists now that Brexit is sort of settled, or at least now that we'll get to see how it eventually plays out.
I agree with you about the lack of community wide grassroots politics in the party, even as a lot of the Corbyn membership surge starts to leave the party. Because why wouldn't they? Party discipline has been a shit show and the inquiries into that have been hamstrung, with the most toxic wreckers remaining in the fold and Corbyn's agenda abandoned.
Starmer's polling is rather hollow with a pandemic on. Not trying to take the shine off it completely, but that's the fact of it.
It remains to be seen what happens from here, jury's out I guess. In Starmer all I see is a deeply uninspiring leader who's reluctant to reveal his commitments.