Brett O'Hanlon it looks like maybe the request to have tasks that are assigned included in the To Do version of "Assigned to me" should begin rolling out in another month (December 2023) according to the roadmap.
https://www.microsoft.com/en-gb/microsoft-365/roadmap?featureid=186228
It says anything where Project and Planner overlap. If you are creating tasks in Project for the Web (soon to be called Planner Premium) then that would be a common function and would allow the tasks to be added to "Assigned to me" when one views their tasks in Tasks by Planner or To Do. My assumption would be that it would only happen on new projects after the update is made, but maybe they will surprise us and it will work on any project that was created in P4W.