A lesson I've picked up from what little localization work I've done is to avoid "specific formats" as much as possible. Some user's locale is never going to fit your "specific format" and the more you try to (micro-)manage the output format of your dates the more you are likely to make that user upset or show them a very broken experience. The short/medium/long formats you can get out of Intl.DateTimeFormat/toLocaleString aren't perfect, they are compromises, but they work and users can generally trust them.

(If you are using a specific format for something other than display to a user, maybe consider the standardized ISO format instead. Machine-to-machine communications could definitely use a whole lot fewer "specific formats" and explicit Date parsing. Very few backend languages don't have out-of-the-box support or easy found library support for ISO format today.)