Silly question...

Not silly but we have learned since that was built. What year?
Yes, the underside of the OSB is a condensation surface but hopefully they have sealed most of the air passages. Unfortunately probably not all as that takes an expensive effort, extra time.

I assume that unfinished attic is fully ventilated thus as cold as outside. But even a small amount of moisture will not be an issue and will dry through the OSB to that attic.

In most cases you do have a vapor retarder from the paint on the ceiling and in most cases they are advising no VB just good air sealing. Citation available.

As for the recessed lights they should be IC and AT rated (insulation contact and air tight) although the air tight is not perfect.

As for finishing the attic into living space it is not grandfathered so check current requirements to be sure you are up to speed. Don't know your location so can't guess. Pictures also help.

Bud

A cape, they are a pain, I live in one. But I suspect they did a pretty good job or air sealing. One indicator is, did they include a HRV or CRV with the house? When a house gets too tight one of those or other fresh air method is required.

One of the problems with a cape is that roofline, the depth of the rafters. They need to be deep enough to install the required insulation and allow airflow from soffit vents to high vents (either gable ends or ridge vents).

Doing DIY without new permits is a risky path. I did some house hunting for someone wanting to relocate in this area and asked each building department is permits had been pulled for the work that had been done. I did not recommend an offer on any of those houses and I suspect the code office was in touch with the owners. Computers today make it easy to track everything.

Bud

Not trying to bust your chops, just need to cover the usual permit topic for you and the thousand readers who come after.

If permits were pulled and no inspection was done then a buyer in the future gains leverage over you because YOU cannot prove the work was done correctly.

Copies of all permits plus copies of all inspections are best. If no one called for an inspection you should have, it's your house and your investment.

Keeping records of all licensed contractors is also a good idea. Hiring a licensed contractor includes their insurance as part of the price. You also want the name and contact info of those insurance companies.

When doing DIY your camera is your friend. Take pictures of all work as it progresses.

Off mu soap box and no need to explain, I'm not part of your project. But i do wish you the best as a fellow owner of a cape. By the way I'm doing a deep energy retrofit on mine and results are impressive.

Bud