The placement of this text suggests "praise, not request" to me too. In fact, we ask for rain separately in the ninth blessing, which makes it seem even clearer that this mention is not a request (would we make the same request twice?).
Ta'anit 3:a cites a baraita that says that both dew and rain are optional. The g'mara asks why, and Rabbi Chanina says it's because wind and dew are consistent:
It is taught in another baraita: With regard to dew and with regard to wind, the Sages did not obligate one to mention them by reciting: He makes the wind blow and the dew fall, in the second blessing of the Amida, but if one seeks to mention them, he may mention them. The Gemara asks: What is the reason that this recitation is optional? Rabbi Ḥanina said: Because winds and dew are consistent and not withheld, since the world could not exist without them, their mention is optional. (translation from Sefaria)
Nonetheless, the tradition now is that we say mashiv haruach umorid hagashem during the winter, not all year, hence the discussions about when precisely to start and stop. Rabbi Chanina goes on to make a distinction between wind and rain, the two elements of the winter text:
Rabbi Ḥanina said: Therefore, since wind and dew are always present, if during the summer one recited: He makes the wind blow, we do not require him to return and repeat the blessing since the wind blows during the summer as well. However, if one recited during the summer: He makes the rain fall, we require him to return and repeat the blessing, because rain in the summer is a curse.
His complaint is specifically against rain (geshem). I can't tell whether he thinks the prayer is actually a request, or if he just thinks we shouldn't be focusing on rain during the summer when it would be unwanted.
(I found my way to these sources from Jewish Liturgy: A Comprehensive History by Ismar Elbogen.)