snuggleshooter's journey

I recently started a management position at a new company after being unemployed for two months, and I'm already facing serious challenges. Initially, my relationship with my manager was positive, but everything changed after another employee was promoted. I’ve noticed a clear favoritism towards that employee, who has been given extra training and opportunities that I am being denied. My manager has been treating me differently than my colleagues. He discourages me from doing tasks that others can do, like asking for positive reviews, and he interrupts my interactions with customers. He often bypasses me when it comes to assigning management responsibilities, which is incredibly frustrating. One particularly humiliating incident occurred when my shirt became untucked while I was helping a customer. Even though no one could see my back, my manager laughed with a coworker and then loudly reprimanded me in front of the customer, insisting that I fix my clothing. He even suggested I needed a larger shirt size and made comments about it being inappropriate to 'flash customers.' This was not only embarrassing but also unprofessional. To make matters worse, I have been written up and placed on a performance improvement plan less than 90 days into my job, without any prior warning. The write-up includes inaccuracies that my manager refuses to correct, insisting that I just need to sign it. He often fails to communicate important information and gives unhelpful responses when I ask questions. He has even interfered with my ability to do my job by moving items out of my reach and withholding information. I feel anxious every time I have to work with him, and I believe his behavior has created a hostile work environment. I’m considering documenting these concerns with HR and would appreciate any advice on how to proceed.