I have also been bothered by this exact question and I have not found an answer inside. The Maharal does deal with this midrash in Beer HaGolah 6:2, but his focus is more on explaining how eclipses indicate sin, especially given that they are predictable astronomical phenomena. My initial thoughts are (1) as @Harel13 says above, I'm not particularly troubled by the Islamic calendar because it post-dates the Talmud. It may also be partly based on the Jewish calendar. See https://en.wikipedia.org/wiki/Islamic_calendar. (2) Even though there are pre-Talmudic cultures that used the lunar calendar, https://en.wikipedia.org/wiki/Lunar_calendar, we could say the Talmud is speaking in generalities and doesn't mean every non-Jewish culture uses a solar calendar.

But two additional problems are (A) the Jewish calendar is based on the moon and the sun. So why don't solar simanim also affect the Jews? This svara would support the first Baraita that a solar eclipse is bad for the whole world. And (B) the Babylonians used a calendar very similar to the Jews, including the same lunar months and a 19-year Metonic cycle of intercalated months. So which "goyim" exactly are they talking about? Perhaps when they say "goyim" they really mean Greece and Rome (which is probably what the Tanaim who authored those Baraitot would have been most interested in). You could probably come up with some nice chiddushim there about the sun and the moon and Jacob and Esau.

I have also been bothered by this exact question and I have not found an answer inside. The Maharal does deal with this midrash in Beer HaGolah 6:2, but his focus is more on explaining how eclipses indicate sin, especially given that they are predictable astronomical phenomena. As @Harel13 says above, I'm not particularly troubled by the Islamic calendar per se because it post-dates the Talmud. It may also be partly based on the Jewish calendar. See https://en.wikipedia.org/wiki/Islamic_calendar. (Though probably at least some Arabs were using a lunar or lunisolar calendar beforehand, which presents the same issue. See below.)

But more generally, Chazal were certainly familiar with non-Jewish lunar calendars. Most importantly, the Babylonians used a calendar very similar to the Jews, including the same lunar months and a 19-year Metonic cycle of intercalated months. Hazal were also familiar with Arabs, who are mentioned in many places in the Talmud, though who knows how familiar they were with the Arabic calendar. (There were also other pre-Talmudic cultures the Rabbis were not in contact with that used the lunar calendar, https://en.wikipedia.org/wiki/Lunar_calendar).

My best explanation so far is that Chazal are speaking in generalities and don't mean all goyim. Or "goyim" may be shorthand for Greece and Rome in particular, given that the statement in Sukkah 29a is a Tannaitic Baraita. You could probably come up with a nice drash about the sun and the moon and Jacob and Esau. (Obviously the Tannaim would have been familiar with Arabs and Babylonians, both of whom are mentioned in Tanakh and Tannaitic sources; my point is they wouldn't have been at the front of a Tanna's mind. In the same way, when American rabbis today say "the non-Jews do such" and such they usually don't mean China).

Another puzzle, not mentioned by OP, is that the Jewish calendar is based on the moon and the sun. So why don't solar simanim also affect the Jews? This svara would support the first Baraita that a solar eclipse is bad for the whole world and pose a problem for the second Baraita that says the Sun is a siman for non-Jews specifically.

I have also been bothered by this exact question and I have not found an answer inside. The Maharal does deal with this midrash in Beer HaGolah 6:2, but his focus is more on explaining how eclipses indicate sin, especially given that they are predictable astronomical phenomena. My initial thoughts are (1) as @Harel13 says above, I'm not particularly troubled by the Islamic calendar because it post-dates the Talmud. It may also be partly based on the Jewish calendar. See https://en.wikipedia.org/wiki/Lunar_calendar. (2) Even though there are pre-Talmudic cultures that used the lunar calendar, https://en.wikipedia.org/wiki/Lunar_calendar, we could say the Talmud is speaking in generalities and doesn't mean every non-Jewish culture uses a solar calendar.

But two additional problems are (A) the Jewish calendar is based on the moon and the sun. So why don't solar simanim also affect the Jews? This svara would support the first Baraita that a solar eclipse is bad for the whole world. And (B) the Babylonians used a calendar very similar to the Jews, including the same lunar months and a 19-year Metonic cycle of intercalated months. So which "goyim" exactly are they talking about? Perhaps when they say "goyim" they really mean Greece and Rome (which is probably what the Tanaim who authored those Baraitot would have been most interested in). You could probably come up with some nice chiddushim there about the sun and the moon and Jacob and Esau.

I have also been bothered by this exact question and I have not found an answer inside. The Maharal does deal with this midrash in Beer HaGolah 6:2, but his focus is more on explaining how eclipses indicate sin, especially given that they are predictable astronomical phenomena. My initial thoughts are (1) as @Harel13 says above, I'm not particularly troubled by the Islamic calendar because it post-dates the Talmud. It may also be partly based on the Jewish calendar. See https://en.wikipedia.org/wiki/Islamic_calendar. (2) Even though there are pre-Talmudic cultures that used the lunar calendar, https://en.wikipedia.org/wiki/Lunar_calendar, we could say the Talmud is speaking in generalities and doesn't mean every non-Jewish culture uses a solar calendar.

But two additional problems are (A) the Jewish calendar is based on the moon and the sun. So why don't solar simanim also affect the Jews? This svara would support the first Baraita that a solar eclipse is bad for the whole world. And (B) the Babylonians used a calendar very similar to the Jews, including the same lunar months and a 19-year Metonic cycle of intercalated months. So which "goyim" exactly are they talking about? Perhaps when they say "goyim" they really mean Greece and Rome (which is probably what the Tanaim who authored those Baraitot would have been most interested in). You could probably come up with some nice chiddushim there about the sun and the moon and Jacob and Esau.