Difference in meaning between "I provide her with a TV" and "I provide her a TV"?

You can also say: "I provide TV for her"

or: "TV, her I provide"

It all depends on how much of a robot do you want to sound like. Or it can also depend on how much like a robot you want to sound.

Let's examine the sentence structure of both:

I [noun] provide [verb] her [direct object] with a TV [prepositional adverb] .

I [noun] provide [verb] her [direct object] a TV [indirect object] .

Both of these sentences convey the EXACT same information. The noun, verb, direct object are the same, and it is up to the speaker on how to convey the remainder - as either a prepositional adverb or a indirect object, which is just a difference in grammar and has no underlying importance in this example.

Neither sentence delivers any information about who owns the TV.

The expression is provide [someone] with [something]. It says nothing about whether that thing is the provider's own, though if that were so, I give her my TV would be a more natural way of saying it.

I provide her a TV is not idiomatic English. We can say I provide a TV for her.

I provide her with a TV, because a TV is a tangible object. I provide for her - no tangible object; support is real but not an object I provide perspective - same as above, nothing tangible