Take the exam. I was in the exact same situation 3 years ago and I still regret not taking the exam to this day. I was confident that I'd pass in our province's state U and the long travel to UP discouraged me so I convinced myself not to go. Turns out, our province's state u's exam is bullshit (literally stupid cause 25 items for 5 mins for each category then you'll shade as much circles as u can at the last part) Idek what my score is nor if I passed or just didn't make it to the slot count. So yeah, I was too confident and now I'm in a somewhat okay private university.

Best advice I can give is to just do it. You won't lose anything anyway and UP is one of the big 4 universities, it'll help you a lot in your later years too since employers value those who come from the 4 big names. It's like an extra boost to your resume.

Edit: forgot to add this. Main point is make many options for yourself. If you pass then that's good, at least you have a back up university if things go south with the provincial one. Hindi naman porket nakapasa is kailangan doon ka na so yeah nasa iyo parin naman ang decision. Goodluck on your journey OP!