I'd be open to making the internet permission "optional" and granted at run-time (if a feature is used that requires it), but that is not supported by Android (as of now).

If I installed SDmaide SE from F-Droid and updating via F-Droid, so in that scenario F-Droid version no longer need internet permission.

While you are right that in some cases like installing from F-Droid, the update check is not needed, but there are also users who grab releases directly from GitHub without any 3rd party app inbetween.

I'm not comfortable with an app that has full network access which handle all system files.

SD Maid is fully open-source, feel free to check the source-code. If you don't trust the me, maybe you shouldn't use the app, there are ways to exfiltrate data even without internet permission. 🤷

Network permission are used mainly for checking new update and message of the day (MOTD) feature.

I believe MOTD is a fancy feature and that's not need necessary for this kinda app.

Both the update check and MOTD are features I want to have in the app, so the internet permission has to stay (for now) 🙁. Maybe a future Android version allows making it optional, then we could revisit this topic.