The second benediction in the amida usually starts "אתה גבור לעולם ה׳". This is not, as far I can tell, part of a verse in Tanach, that prayer books should assume a certain wording or spelling based on its origin. Nonetheless, almost every modern prayer book uses the שם אדנות here rather than the שם הויה. That is, it has the name that looks almost like ארני rather than the name that looks almost like יקוק. I assume, then, that that's accurate: the benediction really does have that name in it. Why? Why is that name used here, when it's so rarely used in general?
As you noticed, in Tefilah Yeshara the shem adnut is pointed.
Somewhat that seems as an answer can be found here in Siddur Kol Yaacov, he said that a shem א-ג-ל-א, who is found in Rashe Tevot Ata Gibbor Leolam Ado-nay. The same reference to this Shem is in Siddur Yaavets (see the comment, the siddur itself does not follow the perush instructions.). In Siddur Shaar Hashamayim from HaShlah, he said sweet gvurot, and also report the shem A_G_L_A
1) This source discusses this issue and suggests that there are different nuschaot, some with the usual form of the name, some with the more unusual form, and explains the kabbalistic basis and implications for the more unusual name.
2) Rabbi Zev Leff writes in his book Shmoneh Esrei: "Alternatively, l'olam can mean 'to the world'...(Rabbeinu Yehuda ben Yakar, in his commentary on tefillah). It is for this reason that God's name is written here as alef-dalet-nun-yud...[it] signifies God as Master of the Creation. The alef represents God's intrinsic existence before Creation. The final yud represents the unity of all of creation under God. This unity is represented by the number 10 (the yud's numerical value), which is the unification of all the individual integers preceding it. And in between these two letters are the letters dalet and nun, which spell din, indicating the finite world of law - the laws of nature that form the boundaries and limitations of the creation."