As far as I can see, Power BI can use a REST API as a datasource:
Unfortunately, Coda APIs for reading tabular data (i.e. the GET /rows endpont) returns a rather complicated schema that isn’t easily mappable to just a list of column->value dictionaries. So you either need an intermediary service to filter and convert the data, or implement a different way to retrieve data from docs.
For the former option you can code the server yourself, or you can use Make / Hookdeck / any other service that can transform and forward webhooks.
For the latter option, I actually have a pack in the works that will allow creating custom REST APIs directly out of your docs on top of the Webhook Authomations mechanism:
To be honest, I’m not developing it that actively these days — it’s on the to-do list but not the biggest priority, as it’s quite an effort for not a large demand. I’m open to getting this sponsored though: if anyone’s ready to pay for this to be expedited I could prioritize this.
P.S. Also you can just export to sheets with one of the packs for this, and use sheets as a datasource if Power BI allows that.