After a recent spell of rain, I noticed my garden was teeming with birds of several different species. At other times I have also noticed lots more birdsong during and after a shower.
I may be imagining this, but is there any connection?
Most birds don't actually particularly like being active during rain, so they may be more active after rain to make up for time spent sheltering (and, yes, some foods may be easier to find after rain).
One of the old country names for the Blackbird is "Storm-cock" named because of it's habit of singing after a rain storm. But don't ask me why they do this!
This name is usually used to refer to the Mistle Thrush rather than Blackbird.