CA
“Is there a מצוה to look good by the גוים?”
I’m not sure what you mean by “מצוה” no I dont think it is one of the taryag mitzvos, and no there is no beracha “…asher kidishanu bemitzvosav vetzivanu likach high ranking position in the goyishe velt”
but it one hundred percent is a positive thing that goyim look up to Jews, As the passuk says “ושמרתם ועשיתם כי הוא חכמתכם ובינתכם לעיני העמים אשר ישמעון את כל החקים האלה ואמרו רק עם חכם ונבון הגוי הגדול הזה ” (to be clear I’m not saying taking a high ranking position is an example of that per se, my point of bringing the passuk, is that we DO care what goyim think of us, goyim saying “עם חכם ונבון הגוי הגדול הזה” is a good thing) This idea that we don’t care what Goyim think is not true.
There are even more examples of the reverse, ie having the Goyim look down at us (and by extension Hashem r”l) is a bad thing examples were brought above. Tachanun is full of such phrases ” לָמָּה יאמְרוּ הַגּויִם אַיֵּה נָא אֱלקיהֶם” “הַבֵּט מִשָּׁמַיִם וּרְאֵה כִּי הָיִינוּ לַעַג וָקֶלֶס בַּגּוֹיִם” and as we conclude ” עָזְרֵנוּ אֱלֹהֵי יִשְׁעֵנוּ עַל דְּבַר כְּבוֹד שְׁמֶךָ. וְהַצִּילֵנוּ וְכַפֵּר עַל חַטֹּאתֵינוּ לְמַעַן שְׁמֶךָ:” There is a lack of kavod shomayim when Jews are suffering, persecuted, downtrodden, looked down upon etc. Thus conversely ,it kavod shomayim when Jews are doing well.
Inyanei dyoma, “looking good by the goyim” even affects haclachic practice (!) The Rema 554:17 says וכן במקום שדרים בין העכו”ם לא יחלוץ כי אם ברחוב היהודים וכן נהגו. Ie when in a goyish street, you can wear shoes on tishaa baav. the MB explains משום העכו”מ שמלעיגים עלינו:.
Again, this isnt strictly speaking “Kiddush Hashem” (thouigh to be fair, phrases change we don’t use the term “chasid” the way chazal do,) and I’m not saying it is a “מצוה” to wear shoes on a goyish street on Tisha b’av. But we very much DO care what Goyim think of us, the Torah and H”KBH