I would expect that pressing tab navigates from the month/year button/ clickable label, then to the next and previous button, then the preceding tab takes the user to the bottom section where the day is selected.
I would expect the days would then be navigated using arrow keys, enter selects the day, and if tab is pressed, the month/year button/clickable label would be focused.

Currently the only buttons which can be navigated to and are interactable using keyboard are the next and back buttons, i.e.:

However, the user is unable to navigate to the 'month' selector or the individual dates:

In addition, if we were to click on the Month label, we also can't navigate or select the month we desire using the keyboard.