If you specifically want to import the document open in preview, try the following script:
tell application "Preview" to set thePath to path of document 1
tell application id "DNtp"
set theDestination to incoming group -- Or use your preferred destination for import.
set theRecord to import thePath to theDestination
-- Optionally, perform a smart rule on the imported file.
-- perform smart rule name name_of_your_smart_rule record theRecord trigger import event
end tell
This script sends the document directly to the specified location in DT. Default is your global inbox. You can trigger it with a single keyboard shortcut, using either (1) an automation app capable of configuring that, or (2) Apple Shortcuts.
The shortcut is defined for Preview only, it is Ctrl+Opt+Cmd+D and not used in Preview - at least cheat sheet tells so. I deinstalled karabiner since I thought something might interfere, but no luck.
On my Ventura Mac, I set Option-Command->(Shift-Option-Command-.) and it works as expected after invoking it once.
However, on Sequoia it indeed acts up. However, this definitely appears to be an Apple issue. Quitting and relaunching Preview causes the hotkey to stop working until it’s manually invoked again. Then subsequent uses of the command only sends that same document.