You are correct in part. She was separately elected but my sense is that she has hitched her wagon to Youngkin (and establishment GOP who are dangling the Presidency in front of Youngkin—VP for her???) and they are acting as a team. If she hadn’t gotten the OK to spout the Liz Cheney/GOP trash Trump line, she would never said such things unless she is a complete dunderhead.
Virginia has a one-term limit for governor. The lieutenant governor has always been the favorite to succeed the governor when that term expires. I'm certain that her plan is to run for governor when Youngkin's term expires. Plus, as another poster pointed out, it would be highly unusual to have a presidential candidate pick a running mate from the same state.