According to Microsoft Support https://support.microsoft.com/help/62031750-a825-4d0c-8bf2-96a585284882. when you add at least one task to a task list in meeting notes, a corresponding plan is created in Planner. This allows you and all meeting invitees to view the task list in Planner. The tasks you add to the first task list in your meeting notes will be automatically synced to the first bucket in your plan. However, if you move tasks out of this bucket, they will no longer appear in the meeting notes but will still exist in the plan. Similarly, if you move a task from this plan to another plan, it will be removed from the meeting notes as well.
To create new task lists in Planner, you can select anywhere in the canvas of your meeting notes and type the forward slash ("/") followed by "Task list."
Keep in mind that within meeting notes, you can only add or modify task titles, assignees, and due dates. For more advanced task features such as checklists and attachments, you should select the three dots and choose "Open in Planner" to access the full range of Planner capabilities.
Regarding the issue of tasks not showing up in the To-Do app, it's possible that the tasks are not syncing properly. Verify if the To-Do app is correctly synced with your Microsoft account. It's worth noting that tasks assigned using Collaborative notes are automatically synchronized with To-Do and Planner, streamlining task management and workflows. https://o365reports.com/2023/05/09/collaborative-meeting-notes-in-microsoft-teams/ 'Note: This is a non-Microsoft website. The page appears to be providing accurate, safe information. Watch out for ads on the site that may advertise products frequently classified as a PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the site before you decide to download and install it.'
As for the question about adding a new plan each time a task is created in a meeting, creating a new task list will indeed result in a new bucket being generated in Planner. Conversely, adding tasks to an existing task list will place them within the corresponding existing bucket in Planner.
In conclusion, ensure proper syncing of the To-Do app with your Microsoft account and utilize "Open in Planner" for more advanced task features. New task lists create new buckets in Planner, while adding tasks to existing lists puts them in the respective existing bucket.