That did it. There was a social share bar plugin that was apparently incompatible with the new version of WP. Thanks for your help!
Thank you. I was able to successfully update the permalinks settings and re-save. There was no problem with WordPress updating the preferences. Unfortunately, the post pages still show a 410 error. I’ve tried to publish a new post as well to make sure that the issue wasn’t just with existing posts and it shows a 410 as well.