I thought that battery charge limitation was a standard Android 12 feature, and that phone should have Android 12. So why do you need that app?
As for what's wrong, I don't know. If your terminal emulator accepts the su command without complaint then it suggests that the shell at least is able to get root access. Which suggests that the problem is with those apps. Just to be completely clear, you have explicitly granted root access to those particular apps, not just checked root access in general? Have you done other checks, such as trying to browse through system directories using a root-capable file manager (at some point that would have to ask for access), or maybe tried Titanium Backup (which I notice has not been updated for a few years, which is a serious sign of how few people root these days)? If some apps on your phone can access root I'm wondering how widespread the problem is, or whether it's just these apps in particular that don't work?