Can flies enter the house through controlled residential ventilation?

These could also be fruit flies. They might have nested in the drainage system during the construction phase.

You only have one plant in the house? Wow!

It is far more likely that the flies come from the potting soil than from the exhaust vent of the controlled residential ventilation in the bathroom! No fly can compete with that.

That's right, especially not such very small ones. Our exhaust air has regularly killed mosquitoes; I always found them when cleaning the filter.

You only have one plant in the house? Wow!

Yes, one in the living area..

Firstly, I don't have a green thumb and secondly, I don't feel like always organizing someone to water it when we're away.

And here is the close-up picture of the fly.

It is not a fruit fly, because I also catch those, when they are around, with the vinegar-juice-dish soap mixture.

Looks like a biting midge. But they don’t go into houses. Hm. I would just clean all the drains and flush them with hot vinegar.

I don't know much about it, but to me it initially looked like a "real fly"/housefly. More than flushing drains, maybe also check filters (perhaps something ran into them and really broke it or is it rotting there? I don't know exactly what they look like, whether that's possible), possibly set traps (sticky things, fruit juice/soap mixtures) or maybe use something scented that they don't like (lavender oil or similar), but I can't think of anything else.