In what senses are 'at' and 'all' used in the phrase "at all"?

I understand that the phrase at all means in any way or in the slightest, e.g. What is the opposite of “to stink” (v)? Is there one at all?, or Not bad at all

I don't understand how the individual words come together to make that meaning.

I understand the use of at as a preposition, e.g.

Are there any apples here?

Can be written as

Are there any apples at this place?

But then what meaning does all take on?

Are there any apples at all?

All is not a place, as far as I can see.

I tried to think of at in the sense of rate

Cornering is not hard at 100 km/h

and that sort of makes sense if you take all to be a shortening of all rates

Cornering is not hard at all

but that doesn't seem to fit the generally understood meaning of at all.

Is there a way to break down the phrase at all into its constituent words that adds up to the same meaning?

‘At all’ means ‘in every way, in any way’ and has been so used for around 600 years. It is now mostly found in negative and interrogative sentences. The ‘all’ element is perhaps self-explanatory. ‘At’ has many uses, not necessarily confined to the location of objects in space and time. They include the now obsolete ‘introducing the reason or consideration’ (OED), which is one possible source for its use in what must now be regarded as an idiom.

While we could study the origins of the phrase, I think the easy answer is, Don't try to look for literal meanings in idioms like this. There are lots of phrases in common use that don't make a lot of sense if you study them piece by piece.

Like, "She was dressed to the nines" means "she was dressed in very fancy clothes". Exactly what this has to do with the number nine I have no idea. "This country is going to pot" means "things are getting very bad". What does that have to do with a cooking implement? Etc.

In some cases you can trace such phrases back and find some sensible origin: a word used to have a different meaning, it is a shortened form of a phrase that as a whole makes sense, etc. Often you hear very fanciful, invented explanations.

If you're a student of language, it can be amusing to study. If you just want to learn to speak understandable English, don't worry about it. Just learn it.