How to write an effective but very gentle reminder email to supervisor to check the Manuscript?

I will just write how I approach the matter with very busy supervisors until now. It has worked without issues and our relationships has not been impacted at all.

The best thing is to take responsibility of the submission process (if you haven't done that already). When you have either the manuscript ready to submit or after you have done the corrections on the reviewers' comments, you can send an e-mail to your supervisor telling him/her that you have done all the corrections and answered to the reviewers (if applicable) and you are ready to submit.

Put a deadline for the submission (not the journal deadline, but yours) and ask him to send his comments, if any, by then. You are planning to submit it on that day, unless you have his comments that require big changes.

Also ask him if he needs to change the deadline, then he can propose a new one. But don't leave it without a deadline, as it could go forever.

"Dr. X:

Your inattention to this matter is impacting my career. Can we please submit this paper?

Thank you"

Sounds like the problem goes much deeper than finding the right wording for a reminder email. Maybe his priorities and time management are a disaster. Maybe he is repelled by your work or presentation style and postponing repeatedly is his way of avoiding an awkward conversation. Maybe you annoyed him in the past so he ignores you now. Maybe you ignored things that he communicated in the past. Maybe he has problems in his private life. Either way, something unprofessional is going on. Your situation would never occur with a well-organized supervisor who is excited about your topic and presentation style.