It seems to me that if there is such a thing as Jewish appearance, it’s not about dress or style but about the visual appearance of specific mitzvot such as tefillin, or actions in general according to Torah commands.
Even what many might consider to be “Jewish dress” is not really Jewish, such as black and white among Ashkenazim, or robes and turbans among Sephardim. Rather these were non-Jewish modes of dress that were adopted by Jews. So why should they now be considered any more “Jewish” than other forms of dress used by non-Jews, like jeans and t-shirts, or even orange jumpsuits for that matter?
It is true that the Torah does not command any specific mode or style of dress (aside from the requirements of modesty which we’re not dealing with here).
It is also true that the visual appearance of specific mitzvot or other actions commanded by the Torah create a particularly “Jewish” appearance.
However, neither of these points precludes the ideal and reality that there be an intentionally distinctive Jewish mode or style of dress.
Upon Yaakov’s return to Israel after his extended sojourn with the wicked Lavan, the Torah refers to him as “shalem”, or complete. The Talmudic sages taught that this term, spelled “shin”-“lamed”-“mem”, was praise for not having changed his distinctive “shem” (name), “lashon” (language) and “malbush” (dress). The same is said about the Jews meriting redemption from Egypt, namely that they were not entirely assimilated into the flesh-pots of non-Jewish culture because they maintained their uniquely Jewish names, language and wardrobe.
These are just a few of several sources which indicate the importance of having and maintaining a particularly unique Jewish mode and style of dress.
Who determines what is considered Jewish dress? The Jews do. Any dress that is accepted by the/a body of Torah observant Jews as their dress makes it the Jewish mode of dress for that group, in that place, at that time.
Naturally, people are influenced by the sensitivities and aesthetics of the culture at large, and Jews throughout the ages adopted modes of dress according to the style and materials that were accessible to them wherever and with whomever they lived. But once it was adopted by them, it became “Jewish”, particularly since Jews generally did modify the local custom in ways that made their clothing in some way different than that of the gentiles.
While you mention the traditional black and white garb of the Ashkenazim vs. the traditional turban and robe of the Sephardim as an example for there being no one Jewish mode of dress, in fact these examples prove the opposite — that Judaism promotes uniformity of dress since nearly all Jews of either of the two major geographical areas dressed basically the same. Furthermore, despite what we retroactively assume to be the similarity between the dress of the Jews and gentiles, the peoples of those cultures themselves were certainly sensitive to, and aware of, the subtle but intentional differences.
Even today, what makes Jewish dress is what Jews wear. Anybody would consider the various black and white combinations that many Orthodox Jews wear to be Jewish dress. But nobody would consider jeans and a t-shirt, or an orange jump suit, to be “Jewish”. The reason is simple — neither is worn on a large scale by observant Jews.
By the same token, theoretically, if observant Jews would ever adopt either as their dress to the extent that it became recognizably associated with the wardrobe of Jews, it would become Jewish dress.
But since that’s currently not the case, but rather, on the contrary, these styles, as well as many others, are found particularly among non-Jews, they are non-Jewish styles. As such, if not prohibited, they should nevertheless be discouraged. For one reason, they look non-Jewish. Secondly, they deviate from what looks Jewish as defined by everything explained above.