Is there any way to automatically enable or disable Tracked Changes in a Word document hosted in a SharePoint Online document library? I've tried searching the available actions in Microsoft Flow/Automate but haven't found anything. If there is not any available action in Flow/Automate, is there an alternative way to do it with the 'Send HTTP request to SharePoint'?
As I am not quite sure about your final goal, I will provide some information about what Flow can do.
Just like you said, using call Http request with Rest API we can get the version number of the file. In other words, we can somehow track the document when it publishes a new version. As we shall make the flow be triggered when a file is modified, simply we can turn on/off the flow as your wish.
And here are some examples getting file version number with flow: https://www.glennprince.com/article/creating-a-version-monitoring-flow-in-sharepoint/ https://powerusers.microsoft.com/t5/Building-Flows/Copy-file-to-location-maintaining-version-history/td-p/274223
I'm a bit late, but I've been trying to accomplish the same thing. It seems that there are very few word doc properties that are accessible to Power Automate.
So the short answer is No, it does not seem like this is possible at the moment.
I have been getting around this by instructing document authors to lock the document with the Protect Document set of options. This can be found in word by going to File>Info>Protect Document. From here you can password lock the document into tracked changes mode. But as stated, this has to be done manually, not to mention I isn't without it's bugs when the document is being shared/reviewed amongst multiple people.
Best of luck