This is an excellent question.
How do we describe the sentence pattern "[subject] + [form of to be] + able + [to-infinitive]"?
I would describe it this way.
We are using an adjective that can take the infinitive. The word "able" is an adjective.
There are many adjectives that can be complemented by the to-infinitive, such as: able, willing, eager, ready, prepared, happy, proud, pleased. [1]
These adjectives can also be complemented by a split infinitive. (A split infinitive is an infinitive in which an adverb separates the particle "to" and the verb.)
Here are some examples:
She is able to carefully read through the text.
She is able to quickly find the answer.
He was happy to publicly praise the president.
The officers are trained to immediately respond.
So the pattern you mention is the pattern of complementing an adjective with the to-infinitive. There are many adjectives that can be complemented by the to-infinitive, and the adjective "able" is one of them.
We can write this symbolically as SVAI, where S is the subject, V is a form of "to be", A is an adjective ("able"), and I is a to-infinitive.
There are many sentences (as shown) that follow this SVAI pattern. If there's a name for this pattern, it might be this: "adjectives that take the infinitive".
Let's look at one more set of examples:
I was easily able to get there on time.
I was very happy to see them win.
This is not the same as a split infinitive, since the adverb is placed before the adjective. But it shows that there are many different ways of using adverbs in these sentence constructions.
Footnotes:
[1] https://learnenglish.britishcouncil.org/grammar/english-grammar-reference/to-infinitives