The author is St. Peter according to Rabbeinu Tam, though some say he only held that view due to pressures of the times.
A good articleanalysis, with citations:
https://www.kotzkblog.com/2016/11/102-did-st-peter-compose-nishmat-prayer.html
https://archive.md/1dPiH
Conclusion there:
...
ANALYSIS:
Whether factually accurate or not, we have established that there was indeed widespread acceptance of the notion that St. Peter had composed the Nishmat, Etan Tehillah and Ahavah Rabbah prayers. This appears to have been supported by Rabbeinu Tam and other Rishonim.
On the other hand this perception was vehemently challenged by Rashi, his student the Machzor Vitry and others who suggested the prayers may have predated the Common Era.
It is interesting to see that the brunt of the debate is played out between both Rashi’s grandson (Rabbeinu Tam) and his student (R. Simcha of Vitry).
In an attempt at reconciling the variant opinions, some suggest that there may have been two Shimons. One was Shimon ben Yona, the Apostle who was known as St. Peter who was viewed rather negatively by Rashi and the Machzor Vitry. The other was Shimon Kipah who was the righteous man who acted as the agent for the rabbis.
But that is just speculation.
In general the difficulty that confronts us is that;
“Since the names of the first paytanim (composers of liturgical poems) have been lost to memory, it has happened that the liturgical poems have been attributed to people who never thought to write them.”[15]
This means that we may never have any real resolution to our question as to who the mysterious author was who penned these prayers.