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An extra Action for the Button Field inside a table (not in the interface), where we can select "Run an Automation"
At the moment there is no direct way to run a simple automation from a button field. it only works on buttons in interfaces.
The press of the button should also "pass" the record ID to the automation, so any automation ran can use the record ID to specifically work on a record.
This is useful for everybody who wants to use the button field in day to day simple operations.