Learn English – He put the keys … the lock after taking it …her bag

It's basically the same as your other question and its answer.

In all your examples here, at indicates an instantaneous event (not related to anything leading up to that event) had an effect; from indicates that the effect stemmed from an existing or long-standing condition.

I became hungry at the smell of the cookies.
The smell of the cookies reached you and you became hungry (instantaneous).

I was exhausted from working all day.
Working all day is a long-standing condition, not instantaneous.

I got excited at the sight of her face.
You saw her face and in an instant became excited.

The last one is more interesting:

I'm broke from having spent all my money at the bar.

Although you could have spent all your money in one transaction, so that you instantaneously became penniless, the use of the continuous having spent means that the state of penury has continued since that time. Consequently you use from.

You could even make a more ambiguous case with

I'm broke from all the expenditure I incurred.

But the same analysis applies: you incurred all the expenditure, and an hour later you had still incurred all that expenditure. It's not the same as suddenly seeing someone or smelling cookies.

What you call phrasal verbs have always been one of the messier parts of English syntax, and grammarians do not agree on what to call them, or how they are put together, or what to call their components.

Your first source is rather old-fashioned in one respect: it calls words like on and in ‘prepositions’ only when they take explicit objects; when they do not, it calls them ‘adverbs’. Other grammarians call on and in used in verb idioms like this ‘particles’ when they do not take objects; and still other grammarians, represented by your second source, claim that they are always ‘prepositions’, but may be used either transitively, when they take objects, or intransitively, when they don’t—just like transitive and intransitive verbs. This last version has the prestige of the highly admired Cambridge Grammar of the English Language (CGEL) behind it; but it is still contested.

Everybody, however, acknowledges that there are three different patterns, and my advice is that you focus on that. You will have to learn every single one of these idioms individually anyway, and will have to know which pattern each idiom follows. Don’t worry about what to call the pieces, just know how the pieces are used.