Ask HN: Worth it to reach out to HR about hiring malpractice?

HN, Always learn a ton from this board so I'm hoping I can get some insight from this. A very large tech company reached out to me about an open contract role on their marketing team in my hometown, and began a series of interviews (four total) culminating with a submitted project that I completed for them to get a better idea of my skillset. Two weeks after submitting the application, I received no response. I reached out to the hiring manager (who would also be "the boss" were I to get hired) and they commented that they had to tie up loose ends with HR. Another week goes by. I reach out again, and received a response a few days later, that hiring for this role has been paused indefinitely. On Monday, I noticed a new role posted. It's now a full-time role, though responsibilities are largely the same. I reach out to the same Hiring Manager, and they confirmed it is on their team. So I applied and let them know that I'm keen to re-start our conversation, especially given I've had four conversations with them and others on their team. Now, I've received an automated rejection to my application. Frankly, I'm surprised such a large org can mismanage their hiring process to this point, and am thinking about reaching out to their HR team to get a better understanding of what exactly happened. I worked very hard on my submitted project, and an opportunity on this team and at this company would be massive, but I'm really shocked and upset about how this transpired. Is it worth it to reach out to HR to, at the very least, get feedback on my work and interviews? I put a lot of time and effort researching this org, and working on the project they asked of me, and to get nothing from it really makes me feel like shit. Thanks HN!