If you want to "flex your root muscle" so to speak, there are options using Xposed modules, but these options do not require it.
Battery full notifications are a bit of a workaround:
- Open Settings and select the Notifications option
- Click See All under the Recently Sent list
- Select All from the dropdown in the top left
- Click the 3 dots in the top right and click Show system apps
- Select System UI
- Click the Battery full item
- Edit the options as desired
As for Device care, that is a little less of a workaround:
- Open Settings and select the Device care option
- Click the 3 dots in the upper right of this screen
- Select Advanced
- Slide the Notifications switch to off
This option may have been part of the Android 10 update. If you do not have this option:
- Open Settings and select the Notifications option
- Click See All under the Recently Sent list
- Select All from the dropdown in the top left
- Click the 3 dots in the top right and click Show system apps
- Select Settings
- Click the Device care (Important) item
- Edit the options as desired
- Return to the previous list
- Click the Device care item
- Edit the options as desired
Keep in mind that this will disable all Device care notifications. If you went with the second method, you may want to try disabling one at a time to remove the notification you want without necessarily removing all of them.