I sailed solo in October. Yes, they are seating all traveling parties at their own tables. The waiters serve you the same as they would anyone else. They are welcoming and amiable, but wouldn't have the time to hover even if they wanted to. You can expect a brief chat with them each day, but that would be the same even if you traveled with others. I've traveled both ways so I know from experience.
I'm an introvert, as well, and didn't find it uncomfortable. Unless you're positively anti-social, you'll likely welcome a few pleasant words with your servers each day. They're not long conversations and they don't hover. I always had a book to read on Kindle while dining, and was very comfortable at meals.
Treat yourself to a dinner at Palo, while you cruise. It's very nice solo, as well. More peaceful than the MDRs.