I remember using some “YouTube video downloader” website (the kind we all used before learning about yt-dl) to download an age-restricted video recently. I had tried several of those kind of sites, and most failed. But one site in particular did allow me to successfully download the age-restricted video that I wanted. Unfortunately, I do not remember the exact website that I had used. And honestly, with what I understand about how volatile these YouTube downloader websites are, I wouldn’t be surprised if that exact site doesn’t even exist by now anyway.

All that to say: try a bunch of YouTube downloader sites. That is unfortunately your best bet at this point. You just have to hope to find one that works with age-restricted videos.