Obtain feedback on rejection by contacting recruiter on LinkedIn

Obtain feedback on rejection by contacting recruiter on LinkedIn I had an interview with a company a few months ago, and I was then rejected. I replied to the rejection email asking for feedback and even sending a follow up, but I never got a response. Yesterday I applied again to a position for which I was a better fit, and got a rejection without interview and without feedback. I put a lot of work in the application and I tried to address the interview of last February in the cover letter, highlighting how I improved, according to what I thought were my shortcomings at the time. I also saw that between the time I applied and the time the rejection came, the job title had changed from X to Senior X, and the hiring form asked "Years of experience in Python" (I put 2), but the job description required proficiency in either Python or C++ (I have 3 years in C++). Any chance this is an ATS error? I honestly think I am a very good fit for this role. I would like to know what skills I would need to develop to become a better fit for them, and potentially reapply another time. Do you think it is professionally fine to contact the recruiter on LinkedIn about this? I was already in touch with them a while ago. I would want to ask feedback on this, and also the past application if that is considered fine, since the positions are very similar. Also, should I let a week or two pass (so that they are less overwhelmed with the hiring process) or do that now (so that they still remember why they rejected me)?