You can have your repeating work items and associated tasks appear in My Week automatically by updating the Resource Planning in the Repeating Schedule of that work item.
Whether you've already created your repeating schedule or are just setting it up, at the bottom of the screen you will see a section called 'Resource Planning'.
If the repeating schedule has already been created, you can access it by going into the work item clicking on the repeating option in the work header or opening it via the Options Menu (...) in the work header and choosing 'Edit Repeating Work'
Once the settings are open, scroll to the bottom of the screen and you'll see the option to update your resource planning. Here you can choose if you'd like it to move into your My Week or not. This will appear the same way if you're creating your repeating schedule for the first time.
The work will be planned for the Work Assignee when the work is created and will be planned for the rest of the Work Team when the Tasks and Budget are created.
Keep in mind that you are unable to update work in the series where the tasks and budget have been created and any updates will not be applied to work items already in your My Week.