I think the air will escape through the lungs eventually.

Gas perfusion into the surrounding tissues and liquids, probably

If your question is about the air: It does! The blood carries a ton of cells that can pick up air components. Red blood cells (more specifically, their hemoglobin) bind to the O2 and CO2. Your vessels also feed into your body's plasma, which can act as a circulating reservoir for yet-to-be-collected CO2.

The major component in atmospheric air, nitrogen (N2), is already abundant in the blood too, so it isn't an issue. If I remember correctly, our bodies are generally in equilibrium with the outside air in terms of N2 partial pressure.

Admittedly, a small air bubble in the blood bypasses a lot of the specialized membranes our alveoli use to make their gas exchange, but blood itself can manage a bit of air just fine.

If you're asking about the nanorobot, however: The article says it's not yet biodegradable to the degree they want to make it.

I’ve seen hundreds of bubbles go into the same person over the course of a couple years of infusions and no issues.

completely anecdotal experience but I had surgery recently and commented on the air in the anesthesia line and the anesthesiologist commented that it only happens in the movies, source: guy who lived

Dr. Google leads me to believe there may be a distinction between air in arteries, and air in veins. The former may be lethal at around 5cc, but the latter may be considerably more tolerant.

My understanding is that these machines are made to not interact with the immune system, since that could cause massive problems - I imagine they expect them to disintegrate in inert pieces that the body can treat as normal waste, like dead cells and the like.

I don't think antibodies can bind to simple materials like these robots seem to be made of.