According to the below articles, it appears that it’s not possible to build a plugin that auto-runs and runs headlessly (no visible UI) without showing a running progress bar spinner, is that correct?
Article Reference https://help.figma.com/hc/en-us/articles/360042532714-Use-plugins-in-files
Running message when trying to run operations after running figma.ui.hide()

If this isn’t possible today, I think it would be a really useful feature that would unlock a lot of new workflows interacting with other apps and hardware that doesn’t necessitate having a UI dialog up and running.