Whether you can send your resume back for an interview depends on how you left your job in the first place. Is it because you were impulsive when you left? How replaceable is your position? Haven't the vacant position arrived since you left? If you think that after you come out, you really can't find a job that is more suitable for you than your original company. If you want to go back, don't send a resume interview. Just ask your former colleagues if you have recruited anyone for your original position. Welcome back. If the company says you are not welcome, don't go back. Even if you go back, it's hard for you to gag others. Do you think it makes sense to work in a company without dignity?
If your original post is still vacant and you need to recruit new people to fill the hole, and there is no contradiction with your unit when you leave, which is a situation of gathering less and leaving more, then I believe the unit will still be willing to let you go back. You asked your former direct supervisor and the human resources department to mediate. Generally speaking, the human resources department will agree with this situation, because it takes time and energy to recruit a suitable job candidate. If it is good for you to betray your personal feelings, HR will agree.
But don't go back by submitting your resume, because once HR sees your resume and thinks that you originally wanted to leave and now you want to come back, it will appear that you are too irrational and ridiculous, but it will have a bad impression on you. If you intercede with HR through your former leader, HR will understand the difficulty of finding a job after leaving your job, but will sympathize with you.
I have been doing HR myself for almost 20 years, and the first-line recruitment interview is also under investigation. Trust me, do as I say. When you successfully re-enter the original company, please remember to invite your mediator, human resources department and colleagues in the original department to dinner, thank them for their help and play the interpersonal card well. As the saying goes, "people are soft-spoken and short-spoken", so that they will not say anything about you in the future, and will understand you and be good for you.