Native English speaker. I started to write up an answer but the more I dig into it the more confused I am.

The subject and predicate need to agree for a sentence to sound normal. “It hadn’t” uses “had not” as the predicate which implies past action and needs a verb to sound normal.

You could say:

It had not installed the tooling.

Or It had not verified that the tooling installed correctly.

In it “It didn’t have” the predicate is “have” so a noun can follow and sound normal.

You could say:

It didn’t have the tooling.

Here is where I’m becoming confused.

Usually you can remove negatives and extra words to clarify grammar. In the sentence “It had the tooling” the predicate is still “had” but it doesn’t imply action so a following noun is fine. Also the sentence “It did have the tooling” is grammatically correct but sounds wordy and would probably be found in a legal document or technical write up. Why does the grammar change when you add a negative? “It hadn’t the tooling” sounds ridiculous but logically it should be fine if “It had the tooling” is fine! This is driving me crazy.

Somebody who paid more attention in English class will have to correct me. I guess we’re just going with " English is weird and it sounds better that way".