Copy and Paste of Tuplets

You don’t have “the beam of a tuplet”. You have the “beam of the notes contained in the tuplet”. Tuplets can contain different rhythm, also without beam.

For such cases as I imagine you are referring to (where all the notes contained in a tuplet are beamed together),

you can make a feature request (creating a new thread and tagging it as feature request). Maybe it could be an extra option that can be switched on or off in preferences that says: select also the tuplet value if the selected contained notes are beamed together or something like that.
The actual behaviour is in my opinion very flexible, but I understand that one can want that extra option. If you search the forum you will see that similar functions was already been requested, for example here:

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