Is it plagiarism to apply for a patent with the scheme put forward in someone else's paper? (The author of the paper has not applied for a patent)

No, that's unnecessary.

If the paper has been published, the patent applied for according to the content of the paper will not be novel, will not be authorized, or authorize the utility model, but the right evaluation report will show that it is not creative. Whether the paper is published or not depends on other circumstances.