"as of" you can read as a short form of:
"as we would say about the following".
That meaning is certainly not time-related; "of" here means "about".
If we look, for instance at you #20: (Keeping in mind we are talking about the adverb on here!)
in the position or state required for the commencement or sustained continuation, as of a mechanical operation ⇒ the radio's been on all night
Dictionaries leave out a lot of text because it would become very repetitive. The full explanation here would read:
"on", as an adverb, can also mean "in the position or state required for the commencement or sustained continuation", as we could say about a mechanical operation ⇒ the radio's been on all night (meaning, the radio has been is a state required for sustained continuation of the radio's function).
As for #28:
performing, as on stage ⇒ I'm on in five minutes
"on", as an adjective, can be used to mean "performing", as people do on a stage ⇒ I'm on in five minutes, meaning I will be performing on stage in five minutes.