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                        Provide localization for month/day
For example, the dropdown contains abbreviations like "Jan", "Feb", "2nd", "3rd", etc.

This is a deep rabbit hole that should be scaled on a per-language basis. Examples of how abbreviated ordinals dates would also be helpful. For example, in Spanish, "Primero, segundo, tercero" can be abbreviated 1º, 2º, 3º.
The glyph that is akin to a degrees symbol is the masculine ordinal indicator for which there is also a feminine ordinal indicator (e.g., 2ª).