Falkon should integrate with KDE and Plasma's file transfer mechanism. Currently it has its own download dialog. Instead the download should be done such that it talks to kjobuiserver and show the download same as dolphin would. This is also done in Firefox and Chrome through Plasma Browser Integration.
In Settings->Downloads, you can choose to use an external Download manager, maybe that's a viable workaround
Agreed, the internal download is OK but since it is now a KDE application it should integrate better with Plasma if it detects it's presence.
The Plasma Download Integration was implemented by this merge request: https://invent.kde.org/network/falkon/-/merge_requests/49 Should be available in: 23.08.0