The issue is fixed. Thanks Tahmid for your attention.
My website is proxied by Cloudflare. I toggled off the Under Attack Mode setting from the Cloudflare dashboard. The REST API issue in the site health disappeared. I resumed the Fluent CRM email campaign and it sent all the emails without any issue.
I saw this on the Cloudflare Community website:
https://community.cloudflare.com/t/cloudflare-blocking-wordpress-rest-api/378792/12
My website is proxied by Cloudflare. I wonder if that’s causing the problem.