[Birthday] Cog model restructure

Restructure cog `Birthday` according to #608. No
functional changes expected.

Command handlers that utilize the `MonthDayConverter` now perform a
"typing cast" to inform static type checkers that the birthday being
passed to the command handlers as `MonthDayConverter` will be
subsequently passed to the corresponding methods in `CommandsCore` as
type `datetime.datetime` instead of `MonthDayConverter`. Note that
Python typing cast does not change or restrict any functionalities
because it is only information to static type checkers.

`MonthDayConverter` now exposes the `InputType` and `OutputType` as type
aliases so that code utilizes the converted can be type-hinted better.

The birth year constant 2020 is moved to `constants.py` as
`DEFAULT_YEAR`.