13 is not going to be post-puberty. Even with kids who shot up and developed early, I'd really struggle to say 15 is fully post-puberty - like it's getting there, and maybe for a few, but there is still a lot of development going on. Many teens will still be very much pubescent at 16.
That said, varying emotions are normal, and people of all ages will have varying wants. I hated going on family trips and did not want to go more when I was 8 than I did at 16. I liked the family trip with my in-laws at 22 far more than what I did with my parents, and miss doing that.
Is it not ENTIRELY NORMAL for relationships between teens and parents to be strained? Parents are trying to parent responsibly, teens are trying to forge their adult identity and push boundaries?
There is a lot of cultural variation in this. In some cultures, yeah, that's 'normal' and expected. In others, not so much and would not be normal. The entire concept of an innate individual identity that needs to be forged and that such forging requires pushing boundaries against authority to be forged are cultural concepts that impact both the responsible parenting and how teens act.
I have three teens and a 20 year old. They've done very little boundary pushing, and what little relationship strain there has been more caused by me and my catching up with new ways to support them as we all changed than any identity or hormone issues on their side.
After puberty kids are racing towards becoming independent adults.
Yeah, no. Puberty is a lengthy process that takes years, it's involves a lot of varying and mixed emotions. While some are at times eager for adulthood, it's also normal for the last thing many pubescent kids want is to be racing to becoming independent adults. I talk to a lot of teens due to my own and my work, and I'm not seeing most really racing off.
Having done childhood on speedrun, living regularly on my own for weeks at a time during much of my teens and left to a new country at 17, I still wouldn't have said I was racing to independent adulthood, I was just surviving and seeking new people to be interdependent with having grown up in an awful environment.