According to GitHub's

I've opened new PRs, toggled the types of merging allowed, and switched my repo visibility to public, but nothing has worked.

CodePudding user response：

I resolved this by applying a branch protection to the main branch. Pull requests raised after that time now show the "Enable auto-merge" button.

This makes sense because, if the base branch is unprotected, the PR would merge immediately after being raised since status checks typically take at least a couple of seconds to report a "pending" status.