This is because of two mistakes/bugs
how to fix is below the explanation
1. The QPKG App is listed in repository under different name, specifically qBittorrent vs QBittorrent
When you open AppCenter, for a split of a second it will show apps (and their icons, names) based on data provided by QNAP QPKG tools (qpkg.conf file and others).
AppCenter will on clicking the store tab icon read and sometimes update repository (XML file) and when it does, which might be in a flash or a few seconds, it will rearrange apps (including their names and icons) based on info from the repository.
The connection between apps in the system and apps in the store (repo file) are made based on QPKG_NAME/"InternalName"
Both the new and the old qBittorrent will disappear from AppCenter when repo file is processed, because the old was removed from repo and the new is listed under misspelled name.
qBittorrent is installed, but QBittorrent is not. qBittorrent (new) is not listed in repo, QBittorrent4 (old) is also not listed in the repo. QBittorrent is listed in repo but not installed (you clicked install on QBittorrent but once it was installed it become to be known as qBittorrent)
2. QNAP AppCenter must not assume all installed 3rd party apps are always present in their store.
When a QNAP Official Store QPKG app is removed (or renamed) from a store, but it's still installed, it shows in "My Apps" tab of QNAP Store tab.
This behavior should be the same for other stores, but it's not. An installed QPKG will not show in AppCenter after it's removed from it's store.
Removed QPKG App from other than official store used to show in QNAP Store (official) tab before. Now when it's removed from the store, it's completely hidden.
to fix: Changes to cached repo file are volatile. You can edit it and fix the problem there, but next refresh will overwrite the repo file. This must be fixed by app maintainer. I would suggest adding old qBittorrent there too to allow start/stop the old app.
specifically: change <internalName>QBittorrent</internalName> to <internalName>qBittorrent</internalName>
and add entry for <internalName>QBittorrent4</internalName> with e.g. <name>qBittorrent old - use new version</name>
to fix - for an user: If the maintainer or QNAP will not fix the issues, you can use this workaround:
Remove the QPKG app store identification.
Doing this will move the QPKG app from QNAP Club tab to QNAP Store (official) tab.
You can do this for both old and new (update might move it back) QPKG apps and they will be visible and allow you to enable/disable/uninstall the app from the AppCenter.
To do this, find qpkg.conf file in /etc/config directory
MAKE A BACKUP
find [QBittorrent4] section for old qBittorrent app
[qBittorrent] section for new version
remove or comment-out the "store" valuename value pair:
# store = a79684706c9e3282fd9972d6737d6287
to see changes, close and re-open AppCenter. You'll see qBittorent apps under QNAP Store / My Apps
Now you can enable/disable/remove