Steps to Reproduce
Type
/scoreboard objectives add something minecraft.mined:#minecraft:logs/scoreboard objectives add something minecraft.mined:#minecraft:logs-> See that the block tag doesn't work.
I am not entirely sure this issue is valid or not, because as seen in MC-132938, and the error about block tags and CanPlaceOn, this could be considered a feature request or an oversight.
There's no statistic for mining any block in a block tag.
This is a feature request, not a bug.