NAD+ research is easier with three questions
What was given, who received it, and what changed? Those three questions do more work than a promising headline.

More NAD+ in blood. Then what?
A study in healthy overweight adults tested oral nicotinamide riboside, or NR. It's a precursor: an ingredient the body can use to make NAD+. Researchers found that it raised NAD+ in blood.
That answers the question about the blood measurement. It doesn't establish that people had more everyday energy or would live longer. If those are the benefits you're interested in, they need evidence of their own.
The study also found no significant difference in reported health problems compared with placebo, a dummy treatment used for comparison. That's useful safety information for this group over the study period. It doesn't establish long-term safety or tell us about injected NAD+.
My question here is simple: is the claim about the blood result, or has a health claim been added? The first is interesting enough without the extra luggage.
A useful muscle result, with limits
Another study tested oral NMN in postmenopausal women with prediabetes. NMN means nicotinamide mononucleotide, another ingredient the body can use to make NAD+. In this study, muscle became more responsive to insulin.
But body composition (the mix of fat and other tissue) didn't change. Neither did HbA1c, a measure of blood sugar over time. Both the improvement and those unchanged results belong in the same account.
So this was a specific muscle finding in a specific group. It wasn't evidence of weight loss, a proven diabetes treatment or a benefit from an NAD+ infusion. A result doesn't become less interesting when we describe it accurately.
Does the bigger claim hold up?
A review of human ageing research found limited evidence of health benefits from NAD+ precursors. It also found that measurements inside particular human tissues remain scarce. Blood is easier to measure; it isn't the whole body.
NAD+ has important jobs in cells. Whether a preparation improves someone's health is another question. Animal findings can help researchers decide what to investigate, but they don't establish longer life in people.
The IV page keeps infusion evidence separate from oral research. If you're looking for amounts, the study amounts page describes two experiments without turning them into a personal plan.
When a claim feels slippery, come back to what was given, who received it, and what changed. Keep the result that did happen beside the result that didn't.
A blood result needs a health question beside it.