I'm currently trying to revisit and check Qt private API usage among packages in Fedora, doing some research what Qt API is used, where it's used etc. to see whether something can be done about it in the future. This is a ticket to track the work around this goal. Currently I have identified some packages that have BR: qt6-qtbase-private-devel, but don't actually seem to use Qt private API at all (verified through a scratch build).
Currently identified packages:

• akonadi-server
• angelfish
• fcitx5-qt
• fielding
• kaccounts-integration
• kf6-kirigami-addons
• kf6-kstatusnotifieritem
• kf6-kuserfeedback
• kf6-qqc2-desktop-style
• kidentitymanagement
• kio-extras
• kmail-account-wizard
• ksanecore
• libksysguard
• merkuro
• mimetreeparser
• nextcloud-client
• optiimage
• photoqt
• python-pyqt6
• qstardict
• xdg-desktop-portal-lxqt

Additionally libfm-qt will need Requires: qt6-qtbase-private-devel added as it's headers depend on Qt private headers.

Let me know in case you know any of these packages in fact need to use Qt private API, it might be a build option that I didn't check, otherwise I will remove this dependency in the near future before doing Qt 6.10 update. I'm also aware that some packages, like python-pyqt6, will need to be tied to the Qt version it was built against and most likely the qt6-qtbase-private-devel dependency was used instead of that.