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Thanks for the message.
I just tested it on my end with both a subdomain and subdirectory multisite setup.
Are you using a subdomain or subdirectory?
If it is a subdomain, you will need to generate a new separate API key for each site in the network (subdomain).
Make sure you have enabled it and set the unique API settings for each individual site.
If you have any questions, let me know!
Thanks,
Elliot