Why does it say "Hodi'a Hashem Yeshu'aso"?
Malbim: When Yeshu'ah and Tzedakah come together in Tanach, Yeshu'ah refers to the action done to save Yisrael, or a general salvation for the entire world, which is the purpose of His deeds and fixing the entire world. Tzedakah is the Midah due to which He enacts the salvation. Divine Tzedakah arouses and causes the salvation. "Ki Kerovah Yeshu'asi Lavo v'Tzidkasi Lehigalos" (Yeshayah 56:1). Tzedakah is always found by Hashem, just sometimes it is hidden and it needs to be revealed. Yeshu'ah is not always found; it needs to come. "Hodi'a Hashem Yeshu'aso" is opposed to salvation hidden in natural means - "Baseru mi'Yom l'Yom Yeshu'aso" (96:2). Here, people need not herald it; Hashem Himself will inform about and publicize His salvation, for it is revealed.
How does "Gilah Tzidkaso" relate to the beginning of the verse?
Radak: It explains it.
Malbim: Also Tzedakah, which is the reason for the salvation (refer to 98:2:1:1), which was hidden until now, now it will be greatly publicized to the nations. His Midah of Tzedakah is one of the three reasons for the wonders. The others are His Chesed and Emunah to Yisrael (verse 3).