Further testing: I exported all my sites (via Local’s export feature and also via the All-in-One-Migration plugin), then deleted the sites from Local, deleted Local, and then reinstalled Local. I tried reimporting one of the sites I exported, but I get a 403 error. Then I created a new site and imported via the All-in-One-Migration plugin, and the site opened without a problem. I also created a new site and left it as is, and it opened fine. However, the Adminer is still giving me the same error message, on both the new (essentially empty) site, and the site I migrated in.
To be clear, both the issue with the Adminer and the issue with the 403 on a site imported via Local are big problems.