Does anybody know why the "How to Run the Flow" option is not available in Record-Triggered Flows? This flow should run in System Context Without Sharing—Access All Data. Currently we have to set Modify All permission to user's profile to make sure this flow runs.
Record triggered flows always run in system mode without sharing, so it is not configurable on the flow itself. The same applies to the Scheduled flow and Process Builder
Recommend reviewing doc
I will reach out to the Salesforce team that owns this feature to have this information added to our documentation too and will update this thread as I have more inputs.
UPDATE: The documentation has been updated to reflect
Record-triggered : System, without sharing
At time of writing this, it doesn't seem like it's currently possible to run record-triggered flows in system mode. You can demonstrate this by creating a flow that updates another record the user does not have edit rights to. That user will receive an insufficient privileges error when triggering the flow.
This is something I found out after recreating several of my Process Builder flows in Flow Designer. I'm assuming this is something they'll change before they do away with Process Builder.