What DLI is on your study permit? You can only study at the college on your study permit unless you change DLIs by informing IRCC. So if you changed DLIs with IRCC to private college, and have been full time at the private college by starting a new program then that is the program for lenght and eligibility of PGWP. For PGWP, you submit completion letter and transcripts for the only school listed on your study permit. Any studies with the other school is not relevant, and not allowed. How many years of months you get for a PGWP depends on length and full time status of one program only.
So if the public DLI, where you are not full-time is the school listed on the study permit then those are the only documents you submit for PGWP.
You CANNOT study at two schools at the same time on one study permit. You are studying without IRCC authorization at one school. So whichever school that is that will not count towards PGWP. In fact, if you include that school’s transcripts, you may be in trouble for studying and working in Canada without a study permit for that school.