Hello there,
Andrew here from the Technical Support team stepping in.
Thank you for your questions regarding the API requests for board restoration and spaces assignment - let me see how I can help!
Unfortunately, the boards cannot be restored via the REST API requests yet - though it’s a good catch that we shared as a feedback with our engineering team to potentially add to their backlog!
As for the boards being added to specific spaces in Miro - this can indeed be done using the Update board request and choosing the project (Space) ID as the new board’s destination.
I hope that helps - please let me know if you have any further questions!