In Esther 4:16, Esther instructs Mordechai:
צ֣וּמוּ עָ֠לַי וְאַל־תֹּאכְל֨וּ וְאַל־תִּשְׁתּ֜וּ שְׁלֹ֤שֶׁת יָמִים֙ לַ֣יְלָה וָי֔וֹם גַּם־אֲנִ֥י וְנַעֲרֹתַ֖י אָצ֣וּם כֵּ֑ן
Fast for me; do not eat or drink for three days, night and day; also I and my handmaidens will fast thusly.
I understand why Mordechai and the Jews should fast; they were the ones in danger, so they therefore had to fast. The same logic would apply to Esther. But why did her handmaidens fast?
We first meet these handmaidens in 2:9 (I assume that the handmaidens Heigai gave her were the same ones she kept as queen):
וְאֵת֙ שֶׁ֣בַע הַנְּעָר֔וֹת הָרְאֻי֥וֹת לָֽתֶת־לָ֖הּ מִבֵּ֣ית הַמֶּ֑לֶךְ
And seven handmaidens who were fitting to be given to her from the King's palace
The Gemara in Megillah 13a discusses why she was given seven (and answers what "fitting to be given to her" means):
ואת שבע הנערות וגו' אמר רבא שהיתה מונה בהן ימי שבת
"And the seven handmaidens, etc." Rava said: she would count with them the days of the week (and would therefore always know when Shabbos was).
For this purpose, there is no need for the handmaidens to be Jewish specifically; further, had Esther specifically requested Jewish handmaidens, she would have given away her nationality, which she specifically kept secret; in 2:10, discussing when Esther was still at the harem, the Megillah notes:
לֹא־הִגִּ֣ידָה אֶסְתֵּ֔ר אֶת־עַמָּ֖הּ וְאֶת־מֽוֹלַדְתָּ֑הּ כִּ֧י מָרְדֳּכַ֛י צִוָּ֥ה עָלֶ֖יהָ אֲשֶׁ֥ר לֹא־תַגִּֽיד
Esther did not tell her nationality nor her birthplace, for Mordechai had commanded her not to tell.
So if even at that stage, Esther was careful not to reveal her nationality, she wouldn't have requested specifically Jewish handmaidens - that would have raised too many eyebrows.
What is the other option, then? Heigai just happened to give her seven Jewish handmaidens? If he's picking them randomly, it's much more likely that few, if not none, of them would be Jewish; if he's not picking them randomly, well, why not? What advantage is there, from Heigai's perspective, of giving Esther specifically Jewish handmaidens?
Based on this logic, then, it would seem that Esther's handmaidens, or at least most of them, weren't Jewish. Therefore, the logic behind the Jews' fasting would not apply to them. So why would Esther insist on her handmaidens' fasting?