Lots of ways to do this!
Two other ideas, other than setting up a prompt with checkboxes:
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To create something that is pretty much exactly what you are describing, including the Palette: Add a "mark macro" action to each of the macros in your desired group, keeping track of the marked state with a variable for each macro, as shown in this thread: Is It Possible to Create a Floating Palate With Buttons That Change Variables? - #8 by Zabobon and then have a separate "executer" macro that reads those variables and executes the ones that were checked, and resets the marked state. You'll need to have some logic to be able to set the mark without launching the macro, I'd probably try dedicating a modifier key, for example:
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You could also dynamically get a list of the macros in your desired group, or any active group, using this excellent macro: AppleScript: How to Get a List of Macros in a Macro Group without the KM Editor Being Activated? - #22 by JMichaelTX , then use the "Prompt with List" action, allow multiple items to be selected, and then execute the selected macros by name from the result of the "Prompt with List" action.
Good luck!