You could create a boolean if it's published or not. (You might even be able to do as a function based on the current date in Baserow - you'll need to confirm, as it's a theory). Something like: IF(date_column = TODAY(), TRUE, FALSE)
I know a little about Baserow, but not a ton. You might be able to pass a filtered URL as your API endpoint to Webstudio, which will only pick up the published items.
If not, I'd try something else like: I'd bind the status code (maybe redirect) using a conditional statement in WS.
My last attempt would be using something like n8n or make.com if the other options are viable.
About Today() It will give a new date every day. On that specific day those links will be live, once that day is over and new day comes, yesterdays Link will be unpublished and new day link will live.
I will check other options you suggesting about filtered URLs.
N8n or make is last option when nothing is working I'll have to go to n8n or make.
I have other option for n8n
I'll save all data in google sheets and with App Script daily triggers I will send one row everyday to baserow table.