The adverb "away" for continuity or repetitiveness

I would like to ask about the adverbial particle "away" meaning continuity or repetitiveness (i.e. not a location, a distance, a change of position etc.).

When used with some atelic verbs, the meaning is "continually, steadily". This part is quite clear to me.

Over the past couple years we worked away on the car in my spare time.

We sat and chatted away till midnight.

The result seems different when away is used with short action verbs, it sounds almost exclusively as "repeatedly" to me. Taking a series of actions somehow differs from going on.

All that can be seen is the silhouette of Macbeth as he stabs away with his dagger.

This reddish-brown bird blends in with the leaves that litter the ground as it pecks away, looking for insects.

No one says a word to me as I bang away on the keyboard.

These feathers serve to brace the woodpecker as it hammers away.

While he rechecked the instruments, getting ready for the afternoon's studies, he licked away at his ice cream cone.

It requires many peck to feed oneself, it would be hard to eat a cream cone with one lick, killing a king requires several stabs.

So, is there such a strict line between the two meanings or is it just me?

The only way of making an instantaneous action continuous is to repeat it.

Thus banging away at a keyboard is made into a continuous stint of action by repeating lots of instantaneous actions.

Consequently you are right that chat away means a continuous period of talking and hammer away means a number of repeated hammerings, but away has the same effect in both cases: it marks the action as occurring over an extended period.

This is a Time Metaphor.
All the sentences in the question refer to passing time by doing various things.

The metaphor theme is Time is Motion in Space. It licenses English speakers to refer to temporal phenomena with words and expressions defined in terms of (their experience of linear motion in) space. E.g,

a long/short time
before/after
put it behind you
look forward to it
years passing
the coming weeks
at this point in time.

That is, long, short, fore, aft, behind, forward, passing, coming, and point all refer to spatial characteristics, not temporal. They are "places" and "movements" in an individual's "progression through" time. Details in Fillmore's Time lecture.

So with these metaphoric verbs, forming a phrasal verb with a particle away uses the sense of time passing, going away, never to return. And the verb phrases simply comment on how the time was passed.

Thus you can dance the night away, sleep the day away, while an hour away, and drink the years away.