Is planner my best option for this request

It's much easier to use Power Automate to create new Tasks in an existing Planner, but you can use it to create a new Planner Creating a Planner Plan and adding it as a tab to the General channel of a Teams team using Power Automate & Microsoft Graph - michelcarlo

You'll want to use a List for the Requests that captures desired name, project date, and the M365 Group to add the Planner to, and then uses that information to create a new Planner. 

I also like to use a second List as the basis for the Tasks: Task Name, Owner, and Days Til Due (as a number, like you've shown above, -1, _2, etc.) to calculate due date in conjunction with the Project Date captured in the request. I like this second list because the flow can create the tasks based on this list - whenever changes are needed, the business can update the List and not worry about touching the flow. 

If there's any room to use an existing planner, with specific buckets and labels for the new tasks, this is by far the easiest way to go. But if different group members are needed, this won't be acceptable.

I hope this helps.