Do you have any hints to figure out the grammatical status of a phrase
more rapidly and consistently?
It is something of a chicken-and-egg scenario, but someone who is learning English, and is trying to understand that sentence from Yeats, could approach it in terms of its clauses, and then "drill down" into the phrases that comprise the clauses.
First the main clause, which can stand on its own without help from any other clause:
The world is full of magic things...
That is a fairly simple predication with "is". The world is full. What is the world full of? Magic things. There are many magic things in the world.
and then the relative clause:
...patiently waiting for our senses to grow sharper.
To what do we attach "patiently"? To the world, or to the things? To the things. Those magic things wait patiently.
The present participle in a relative clause might be understood as a variant of a "which-clause" with the simple present:
The world is full of magic things which wait patiently...
The world is full of magic things waiting patiently... (or patiently waiting)
There is an "invisible" or "implicit" predicate of sorts there: things wait.
He looked at the old cabin sitting in the clearing.
The cabin sits in the clearing.
What or whom are those magical things waiting for?
They are waiting for our senses.
What does it mean, to wait for our senses? It is almost meaningless. Without the infinitive phrase, it does not make much sense:
...to grow sharper
Those magic things are waiting for our senses to grow sharper.
She was waiting for the celebrating.
She was waiting for the celebrating to begin.
When our senses grow sharper, we will be able to see and hear the many magic things that fill the world.