Is "provide" in "provide against something" an intransitive verb?

From Cambridge Dictionary:

provide against something

phrasal verb with provide verb

to make plans in order to prevent or deal with a bad situation

From OLD:

provide against phrasal verb

provide against something

​(formal) to make preparations to deal with something bad or unpleasant that might happen in the future

From M-W:

provide against

verb

to do what is needed to prepare for (something bad that might happen)

From Longman:

provide against something

phrasal verb [transitive] formal

to make plans in order to deal with something that might happen

From OED:

I.2. c1425– intransitive. To take appropriate measures in view of a possible event; to make adequate preparation for the future. Frequently with against, for.

From Collins:

(intr; often foll by for or against)

to take careful precautions (over)

She provided against financial ruin by wise investment

Four dictionaries classify "provide against" as a phrasal verb used to make preparations for unpleasant events, and they categorise it as a formal expression rather than an idiom. Cambridge, OLD, Merriam-Webster, and Longman treat the combination as transitive, whereas the OED and Collins describe "provide" as intransitive when followed by "against".

Within "provide against something", should I regard "provide against" as a complete transitive verb, or should I analyse the individual function of "provide"?

Does "provide" have a direct object? Consider a sentence like:

Beach operators do not have a legal obligation to provide against injury.

No. A direct object is an NP that follows the verb. This verb is followed by a preposition. The verb "provide" does not have a direct object.

Hence intransitive.

"Provide against" is both a formal expression (not colloquial) and an idiom (an expression that has a particular meaning different from the meanings of each word on its own). All phrasal verbs are idioms. Some are formal, some are casual.

Generally, modern grammars treat phrasal verbs as idioms rather than compound words. That is in the example above, "injury" is the object of "against" rather than the direct object of [provide against]. Older grammars sometimes take the alternative view: that [provide against] is a verb.

But either way, "injury" is not the direct object of "provide". The word provide has no direct object and hence must be intransitive.