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PowerBI API throttled
It clearly states here Power BI Premium capacity load, overload, and autoscale - Power BI | Microsoft Learn that your requests will be treated as second class citizens.
See the limitations section. Export Power BI embedded analytics reports API - Power BI | Microsoft Learn
It does not mention anything about a maximum amount of parameter updates in the documentation for the API call: Update Parameters In Group
It is also not an issue with exceeding the maximum amount of refreshes in a day (seeing as though it needs to refresh the semantic model after every parameter update API call) because the error specifically happens when I try to update the parameter; not when I try to refresh the semantic model afterwards.
In the linked documentation I also find no potential issues that my export script would run into.
It clearly states here Power BI Premium capacity load, overload, and autoscale - Power BI | Microsoft Learn that your requests will be treated as second class citizens.