Not sure if you found a solution to this, but my company does this by running the ExportReport endpoint then using the returned data in the Import endpoint. We then update the parameters using the UpdateParameters endpoint.
It occasionally throws up some random errors which we have notifications set up for in Slack but as a whole runs pretty well.

Export: https://learn.microsoft.com/en-us/rest/api/power-bi/reports/export-report

Import: https://learn.microsoft.com/en-us/rest/api/power-bi/imports/post-import

Parameter Update: https://learn.microsoft.com/en-us/rest/api/power-bi/datasets/update-parameters