Remove the old code first, keep only the data/ and config/ folder. Then extract the new code and run the occ command.
Your description sounds good. You are sure that you downloaded the right archive (check the version.php in the main directory, it should show the version string of NC 10.0.1)? Your config/config.php should still contain the old version string as you haven’t upgraded yet.
If you go to the admin page, which version is shown there?
Other idea is that the version is somewhere cached. Can you try to restart the server and see if it solves the problem?
You can download the apps manually from apps.owncloud.com. The new nextcloud app store is only testing and probably doesn’t contain all apps yet (New App Store: Nextcloud 9/10 Testers Wanted!).
I mark your last topic as “solution”. Try to find the issue and let us know if there is more to be considered during the upgrade process.