The new Update custom field action, in Automation, can update text and number types fields, but can't update a date field. This is probably due to the fact that it may be hard to convert a text string to a date, or at least, to recognize a date format in a text content. A workaround could be to create a Custom code action (using JS, python, ...) : we could use variables (previous steps) as inputs, and process them to return a value (text or number or date).
