IIRC Time Turners can’t change the past. Whatever actions you do while in the past have already happened the first time around, you just didn’t know it because you didn’t travel to the past yet.
Correct.
https://en.m.wikipedia.org/wiki/Novikov_self-consistency_principle
Within that framework, HP timetravel is self-consistent and, say, Back to the Future and others of that type aren’t.
Very well shown in Rick & Morty snake timetravel episode. The snakes do the inconsistent time-travel and Rick only does consistent.
Time turners can’t change the past that you observed and even then it could’ve been an illusion or a trick. Dumbledore could’ve gone back in time to save Sirius and then cast an illusion making everyone believe he passed through the veil. The past didn’t change, only people weren’t aware of what was really happening.