Look internally for positions you might be interested in. Note to your manager that you are applying for one and would like their assistance and aid in transition of your responsibilities.
HR is an absolute do not engage.
HR is for labor issues and they represent the firm. Unless you have an actual case against your manager, with evidence, and seek to remove them from the company, HR will do nothing unless it protects the company.
For the position, many managers are very reluctant to consider an employee who doesn't get along with their manager, regardless of the circumstances. And not informing your manager is a problem. The interviewing manager will contact your current boss and your current boss will be surprised and speak ill of you for that alone.
It's a bad set of circumstances. And not good for the health of the company.
Separately, do not start the process without an exit strategy. Be ready to be dismissed or constructively discharged or overworked. That means documenting everything offsite. Copies of emails, call recordings, contemporary notes. Anything that might be used to show actionable items for a complaint post termination, including positive reviews and feedback.
You are correct that the situation is irredeemable, and I say this knowing nothing other than what was written above. It's just a story I hear daily from both sides. As a people leader I am frustrated.
Good luck.