I have now figured it out.
You must import / create your project that you wish to be the template in project for the web.
The next step is to mark the project as inactive (read-only). It seems the CopyProjectV3 action will only accept a project to copy from that is in an "inactive" state.
Navigate to your Dynamics 365 App, click the "Dynamics 365 - Custom" Title.

Select Project.
You should now be looking at a list of "active" projects.
Check the project that is to become the template and deactivate it:

While you are there, grab the projectid by clicking the project and copying from the URL:

This will be the the project ID that is used in the power automate flow field.
Next is to create your power automate flow.
Begin a new flow with whatever trigger you desire, in your instance klarson, you will need to create the trigger "When an existing item is modified".
Then add a step "Get changes for an item or a file (properties only)" using the ID from the trigger.
Add a Condition step to check if "Ready to schedule" is equal to "Yes".
If Yes > Add a new step "Perform a bound action", the action being "msdyn_CreateProjectV1".
Fill in the subject, and any other details you want to pass through for creation of the new project.
Add a new step "Perform a bound action", this time the action being "msdyn_CopyProjectV3".
The Row ID should be the ID from the newly created project.
Scrolling down, the "msdyn_project msdyn_projectid" field should be the project template ID we obtained at the beginning.
I set "ReplacedNamedResources" to yes and viola. You now have a new project that contains all the tasks, etc from the previously created template project.
Let me know if you need further details on any of the steps and I'll try to help.
Enjoy!