Are these pages indexing in Google? Are they in search results?

Remember to use: <link rel="canonical" href="https:url" />

Yours <link href="https://example.com/test-me.html" rel="canonical"/> looks fine to me, but version mentioned above is recommend by Google.

If pages have self-canonicals (so canonical links are the same like pages URLs, where canonicals are located) it is all right. There is no problem to solve.

"Canonical same" it's just an information, not an issue.

If pages are indexed in Google, you need to do nothing with it. :)

The exception is if you don't want to index the pages, and they are in Google search. In that case, let me know and I can help.