I think you just stick to this extra table.
Create a relation from the Places table to the Favorites table, and return all the emails through a joined list column.
For favoriting/unfavorting:
Favoriting: Add a row to the Favorites sheet, containing the signed-in user’s email and the Places ID.
Unfavoriting:
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Add a template column in the Places table containing the email of the signed-in user and the Places ID. Let’s say it would look like: a@gmail.com - ID.
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Add a template column in the Favorites table with the same structure as above.
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Create a relation using the pair of columns above, from the Places table to the Favorites table.
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When people click an “Unfavorite” button, you delete the row using the relation. That way, you can just always refer to the list of emails I mentioned at the top to pass to Zapier, no need to care about adding/removing elements from arrays.