Typically, to perform the enabling and disabling of measures immediately on demand, those measures would need to also be updated after enabling / disabling them, otherwise the enabling / disabling will "wait to happen" when the skin is updated (i.e. it will "lag" a bit).
Now, if you add [!UpdateMeasure SomeMeasure] in the LeftMouseUpAction, you'll see how the toggling happens immediately, in other words it has an effect, if you were to have two opposite such toggling bangs following one another.
In your code, you mostly don't update measures after enabling / disabling, hence disabling a measure right after enabling it like I mentioned will make the enabling not happen at all because by the time the skin is updated the most recent bang will be the disabling one (which is why I said that the construct doesn't make sense).
That being said, for WebParser parent measures, you'd want to enable and possibly
command that WebParser to update (regular measure updating doesn't make a WebParser parent retrieve data, it only updates the value of its options), and then if you want disable the said WebParser in its FinishAction. See the below for an explanation of how WebParsers update:
https://docs.rainmeter.net/tips/webparser-updaterate/