Scheduled refresh error "This dataset includes a dynamic data source" with different base URLs

Update: I tried setting up a Power Automate Flow for this, but it doesn't seem to work. Everything says it's successful, but then nothing updates.

What are my options for setting up a scheduled refresh? I could try to learn the REST API to set up a scheduled refresh, although this gives me pause:

https://azure.microsoft.com/en-us/updates/power-bi-embedded-analytics-rest-api-schedule-refresh/

"Note that this API is relevant for cached (import mode) or composite models only."

I don't know what that means, but I'm getting increasingly frustrated with each new approach to this problem and failing. I just want to do a scheduled refresh with a variable in the base URL. You'd think this would be easier, buuuut

Any help would be much appreciated. Thank you!