We have had a system in production for a couple of years now, however, in the last week or so we have observed that the Move File action in Flow results in the moved document being assigned a new Document ID when the Document ID Service feature (https://support.office.com/en-gb/article/enable-and-configure-unique-document-ids-ea7fee86-bd6f-4cc8-9365-8086e794c984) is enabled in the Site Collection. This is a change in behaviour for the action as this was not happening previously. To compound this, the native "Move to..." action in the UI works flawlessly and preserves the Document ID assigned to the item.
Below is a screenshot of "LibraryA" showing 3 documents, each with a value assigned to "Document ID" by the Document ID Service. I have duplicated these values in a text field called "DocumentID History".
I have a Flow that is configured to run when the file is created/modified and a Yes/No field (not shown) that permits a document to be moved, via the Move File action, from LibraryA to LibraryB.
Below is the screenshot of after "DocA" was moved via the Flow and "DocB" was moved using the native "Move to" button in the Action Bar.
Notice that the Document ID value has been replaced in "DocA" but not "DocB". This behaviour was not happening a week or so ago and so represents a change in the way the File Move action appears to be working.
I have raised a ticket with the Power Platform Support but thought I'd share this with the community now.